Under normal circumstances, a user cannot view deleted posts without the "Moderator Tools" privilege. However, I noticed now that I can view the now deleted question to which I had previously posted (and deleted) an answer.
Does the fact that I posted an answer allow me to view it, or is there something else going on here?
It's because you answered it, yes. You can always see your own deleted posts if you have a link. Because it doesn't make sense to see an answer in isolation, if your deleted post is an answer, you see the question too. (And any other answers, I suppose; I don't think there's code to show subsets of pages like that.)
You can see your own recent deleted questions from the "show recent deleted posts" link on your profile, but for older posts you would need to have saved a link.
I believe the developers are trying to strike a balance between letting you have access to your own work (so you can "rescue" it if you want), on the one hand, and leaving reminders of old deleted content around forever where people can dwell on it, on the other.
