Billy's harsh words is an article in Resident Evil Recollections. It was uploaded on 28 January 2016.
Billy initially declines to team up with Rebecca at the start of Resident Evil 0 as he doesn't want to be arrested.
A little later he tells her try and "go and try while I wait here.", although at this point I'm pretty sure he knows there's no way she'd be able to face whatever's up there on her own.
I suppose he's trying to teach her a lesson on cooperating, but I can't help feel that it's every so slightly malicious all the same.