if someone sober had sex with me in a state they described as “paralytic”
It's his own description. That's the thing, isn't it? It doesn't really matter what each of us has done while drunk, how any of us sees the finer points of drunken consent, or what exact words OP's boyfriend used. It doesn't even matter whether she felt, the next day, that she'd not only consented but insisted.
The fact is he deemed her unable to consent.
This isn't 2020s sensitivity-informed hindsight, either, he knew at the time but wasn't 'strong' enough to resist fucking a woman he believed was non-consenting.
This in itself is very worrying. Now we've also got concerns over why he's landed this on you, @Inengland, yet not on the woman he believes he raped. And why it still looms large in his mind 15 years later. So large, in fact, that he just had to tell you about it after knowing you for only three weeks.
He must have told his previous girlfriends this story, or a version of it, however many women he's dated in 15 years. Has he never been able to talk to anyone like I can talk to you? Bullshit. He puts his 'I was nearly a rapist' guilt story, or a version of it, out every time.
The question is why he does it. Up to you if you want to stick around and find out the hard way but, as @MsJinks says, It’s strange - but useful - guys do this. In my experience, and many others, they're telling you something they've done far more than once and intend to carry on doing.