I have the impression that Hitomi threw the match, even though a blow to the skull would normally be effective vs honey badgers, because of Oshie's remark about her being able to move her left arm, and Hitomi not using her origin form (and fighting seriously like vs Kido and vs Tasuku); throwing the match was also what Leo apparently did back in the beginning, to allow him to attack a greater enemy. Hitomi originally wasn't meant to participate on the Deathtival/Destival, back then she joined it to keep an eye on Nomoto and then for fun/seeing the "other Uzaki", but now she might see Yashin as a threat to Shidou and herself.
It could also be that she didn't think of anything other than fighting as many fights as she can, not even paying attention to who's near her, just getting said person (Nomoto) out of the way, and not being able to fight seriously because she underestimated Haiji and paid the price for it (wouldn't be the first time, either), being too badly injured and too late to make a comeback, even if she fights to her last breath.
About Kaede's remarks, what's important isn't the occult aspect, but Haiji's characteristics of being abnormal, being able to fight fearlessly and without regard to disadvantages or deeper motivations (at least until she found out that Hitomi was her childhood friend and wanted to make her feel fear).