Looking if that's the case, would he have carried on shooting? Wouldn't he have stopped in horror and tried to save her?
I don't want this to be the case, but because of all the strange things - not just one or two things but loads of odd things - I do think he knew it was her. I just think that they had a massive disagreement, I think he told her to f**k off from his house, she was dressing to do that, and his rage overtook him. He has shown rage in incidents before he met her and I think he is/was volatile and unpredictable.
There are many elements that go to make up OP - his disability, his love of firearms, his sporting prowess, the adulation of him by others, his fame, and all of this goes to make him the person he is and has contributed to this awful scenario. When everything is going well you give people the benefit of the doubt, he overcame enormous odds to become an olympic success and an icon, so people overlook the drunken boat incident, the boorish behaviour, the volatile character etc... blowing off steam, just Oscar being Oscar etc, but then there's a dead woman in his bathroom and it all changes.