It only corroborates his story if LE can produce pictures and some testimony from a medical person that would be willing to state that those injuries are at the least consistant with having your head hit against concrete. Not a lay person but a medical person, they would have to have been taken while he was in custody, since anything that is dated after he left the Police station is just not evidence that he was injured that night...he could have been injured later on that morning and then gone to a doctor
There is a reason that Police do things by standard procedures, they document all injuries, with photos and rulers for scale from many angles and get all medical documentation, it is NOT at all unusual for people to injure themselves and claim that someone else did it, if LE did not do that in this case then we are left to believe that they didn't really see anything worth documenting, or they just really really dropped the ball, and they all need to be fired and a whole new department hired
FWIW those injuries are way too far up on his head to have been from having his head hit against concrete, he might have been hit in the head with concrete and gotten those, maybe and that video was actually damning as far as the broken nose IMO and I have seen quite a few broken noses IMO JMHO and stuff.