Thats what I thought too, but she really didn't describe it very well or explain it clearly. I had to reread that part a few times because I was so lost.
I think in the other books, he was looking into a pensieve that already had memories put into it. Dumbledore had one that he would occasionally add to, so Harry literally just stuck his head into it and watched. I suppose with Snape, he wouldn't just leave his memories laying around for anyone to watch so he leaked them out for Harry so that he could view them and learn the truth? That seems to make sense.
Both Dumbledore and Snape had pulled them out at will in previous books, so I don't see why he couldn't make that happen.
I know I've read about them pulling them out one at a time ad putting them into the pensieve, but it seemed weird to imagine them leaking out in a bunch of fluid everywhere. I think that's what threw me. I immediately imagined unicorn blood instead and thought that maybe Snape had used some and that it was leaking out now that he had died. It wasn't until I read later about Harry using the pensieve that I went back and re-read it and figured it out. Maybe my brain just works in a strange way!
I actually think that he did it not to show Harry that he was on the side of good, but to give Harry a reason to willingly walk to his death (and thereby fulfilling his agreement with Dumbledore). I honestly believe that Snape didn't care one iota what Harry thought about him.
I think you're probably right about Snape. Seems to me that he clung to his dislike for James through Harry to the last, but owed it to Dumbledore to see that Harry actually fulfilled his destiny.