Most of the time, I'm willing to give them the benefit of the doubt on their research unless there is something VERY obviously wrong (like Agumon being given a weakness to Earth elemental attacks, which was only done in one single Digimon game and was also something never shown with Tai's Agumon partner, and only using Tai's Agumon partner to explain abilities and feats and don't include Marcus Damon's Agumon partner, but they use several different Charizards - Red's, Ash's, and Alain's - for Red's Charizard's profile). Not to say that I believe they're 100% right and are flawless in their research, but I also don't think it's based on popularity either or else Red and Charizard would have easily beaten Tai and Agumon, or Mega Man would have beaten Astro Boy, and so on.
In this case though, from what I've read online and seen others able to actually explain (not just claim), they did miss a bit with Ichigo in this match-up.
I am about 75-25 about Death Battles credibility on their fights mostly because there are some fights, like you said, that they either forgot some info or they exaggerate some info for one character. I don't know if it is out of bias or misinformation, but if it is Bias, then Goku would have won against Superman and yet didn't. Though, to be fair on that, it was actually the fans that provided the information to DB and not DB doing it themselves.
Death Battles I agree with:
Boba Fett vs Samus: Samus is totally more powerful AND has more going for her.
Akuma vs Shang Tsung: This one was difficult, but I can see how Akuma would barely win.
Goomba vs Koopa: Both are canon fodder
Haggar vs Zangief: I hate to admit this one, but they were right.
TMNT 4 way: Yeah, Leonardo would win
Zitz vs Leonardo: Again, I would agree. Leonardo is a beats at times
Yoshi vs Riptor: I agree though not sure why I do. Mostly because Yoshi is like the Bugs Bunny type character
Felicia vs Taokaka: Definitly. Taokaka is childish, but deadly when angry
Kratos vs Spawn: No contest for Spawn..
Bomberman vs Dig Dug: Yeah, Bomberman was too squishy for what he can do.
Vegeta vs Shadow: Vegeta rocks. Renegade4life
Mario vs Sonic: Sonic had to win this easy just because he basically could go Super Saiyan
Luke Skywalker vs Harry Potter: The kitten you can see Luke do...at least what he did in EU before it was deemed not canon...was beastly. He was the most powerful Jedi ever.
Chun Li vs Mai: I totally agree with........*drools* nyyyuuuuuhhhhhhh hot girls......
Starscream vs Rainbow Dash: "This is a pony. A baby horse girl's toy. Why is it so awesome?
Master Chief vs Doom guy: Master Chief is definitly a more refined soldier.
Eggman vs Wily: Villian on Villain beatdown
Thor vs Raiden: God of thunder indeed
Batman vs Spider-man: No contest, Spider-man wrecks and thank god they don't do what fanboys do and give Batman prep-time vs Spider-man no prep-time.
Goku vs Superman: Definitly. This is the one that is the most legit because they used the fans themselves to gather info...not their own team. If Goku lost, it is because his fans let him lose.
He-man vs Lion-O: Basically the Diet Coke of Goku vs Superman
Shao Kahn vs M.Bison: A man with soul powers vs a man who east souls for breakfast...literally. Yeah no contest.
Ryu vs Strider: I wanted Ryu to win, but seeing how Strider is far more powerful. Again, Ninja Goku vs Superman.
Ivy vs Orchid: More girls...more fun.
Fox vs Bucky: Close call, but Fox can take on far more than Bucky can. I love how Bucky killed Slippy
Terminator vs Robocop: Robocop was fine.
Luigi vs Tails: Luigi is actually far more powerful than Mario, but tails is weaker than Sonic.
Pokemon battle Royal: Proof that Ultimate defense is game. Go Water Bowser.
Fulgor vs Sektor: Fulgor is just beast. ULTRA-ultra-ultra-ultra
Tigerzord vs Gundum Epsilon: Bad ass. "I'll BREAK YOUR FAAAAAAACCEE!!"
Ryu vs Scorpion: Scorpion is also just too powerful. He doesn't die, he just goes home. He is the Kenny of the MK universe
Deadpool vs Deathstroke: Again, proof that defense can outbeat offense. Especially if one cannot be killed.
Kirby vs Majin Boo: Kirby is just....PINK!!!
Ragna vs Sol: I love Ragna, but Sol....he is a beast...no pun intended
Gaara vs Toph: I know Toph was gonna win because I know how powerful Toph was. She can control sand too.
Chuck Norris vs Sagara: Too funny. Funny how hey made an appearence in Naruto vs Ichigo
Guts vs Nightmare: Guts is a man who is just sick of their kitten.
Beast vs Goliath: Come on....this one was obvious
Solid Snake vs Same Fisher: I wanted Sam to win, but Snake is definitly better. Though Sam might live longer.
Donkey Kong vs Knuckles: Again, pretty obvious
Wolverine vs Raiden: Rules of nature.
Hercule vs Satan: The biggest loser indeed.
Mega Man vs Astro Boy: Astro Boy is the OG
Green Arrow vs Hawkeye: Though I do call BS on Hawkeye a bit
Charizard vs Agumon: Agumon is far more powerful, but yeah they did kind of overplay some things.
Dante vs Bayonetta: Dante is just unkillable though I see these two mostly being lovers than fighters. "How come I never meet any nice girls?"
Bowser vs Ganon: POWER.
Flash vs Quicksilver: Flash is far faster.
Joker vs Sweet Tooth: Joker is just...too sadistic to die.
Meta vs Carolina: Ah good ole red vs blue.
Cammy vs Sonya: MK always seemed more powerful than SF
Tracer vs Scout: Quantum Leaps in differences
Ken vs Terry: I love Ken, but Terry even trained Rock Howard who is my favorite character.
Hulk vs Doomsday: Doomsdays is unkillable for a reason and people forget that Hulk is powerful, but not as powerful as you would think.
Zoro vs Erza: This one surprised me, but I get why Zoro won.
Deadpool vs Pinkie Pie:.........I...I don't even...
Lara Croft vs Nathan Drake: Lara is unbelievably powerful
Scrooge McDuck vs Shovel Knight: Uncle Scrooge is cheaper than Mr. Krabs.
Venom vs Bane. Venom can match Spider-Man...nuff said
Power Rangers vs Voltron: Form blazing OP sword.
Natsu vs Ace: Funny how Ace lost this one
Sub-Zero vs Glacier: Sub-Zero all the way man.
Ballrog vs TJ Combo: Combo breaker
Shredder vs Silver Samurai: There is a reason why shinobi were made to fight samurai
Smokey Bear vs Scruff McGruff: Only you can prevent burns
Thor vs Wonder Woman: I knew WW would win, but again this puts disbute for WW vs Rogue
Death Battles I disagree with:
Rogue vs Wonder Woman: While Rogue can absorb powers, I feel WW is too fast and too strong for Rogue to handle. She couldn't even absorb Juggernauts power without problem.
Zelda vs Peach: They used an ability for Peach from basically a non-canon game that made no sense....so yeah....
Link vs Cloud: I disagreed with this one so much because they gave Link everything and gave Cloud only his basic gear. Plus, Cloud is an RPG character and they are very hard to gauge in battles.
Batman vs Captain America: Again, I found BS with this one because they downplayed Captain America and used ONE PANEL to decide the victor rather than the actual history. I feel Cap had a better chance in the long run.
Yang vs Tifa: Again, Tifa is far more powerful than they made her and Yang is much weaker than they made. Even Monty said their was a limit to Yangs abilities, but this was before Yang got her arm cut off.
Death Battles I am unsure about:
Pikachu vs Blanka: I have played Street Fighter, but don't know much about it so I can't be sure about the info.
Godzilla vs Gamera: I don't really know these two. I have ehard of them and seen them one, but not their full history.
Iron Man vs Lex Luthor: I really don't know who would win this really. Though Iron Man has become broken recently.
Darth Vadar vs Doctor Doom: This is also a difficult one for me.
Ratcher and Clank vs Jak and Dexter: I don't know them, I know of them, but not their own abilities.
Mewtwo vs Shadow. Yeah I am not sure.
Amy vs Ramona Flowers: Don't know them and Amy always was weak to me.
Android 18 vs Ms. Marvel: I didn't know 18 had some of those abilities and really confused.
Now for Naruto vs Ichigo....I feel they gave Naruto too much credit in abilities like being able to use elemental attacks. Well, yeah, but he doesn't use them outside of Rasengan and he is worse than Goku when it comes to abilities. Ichigo, I believe, had a better fighting style AND Naruto kind of got his as kicked by a 12 year old girl. Where was all that power with that one huh?