How can I tell this person that I don't remember this confession at all. If I would have remembered it, it would have been an important memory (even though I would have rejected it at the time).
I think you should leave the bolded part out completely. I know you don't want any "don't do this" advice, but I think the most hurtful thing to say in this situation is "I don't remember because it wasn't important then, but it is important now." This makes it seem like you don't really care about the other person, when you've said in your question that this is not the case. The fact of your situation is that you don't remember, and whether or not the memory is important is irrelevant to your memory of the event in this case. If you value this other person, I suggest you leave out any remarks on how important the memory would have been. It's simple enough to say "Sorry, but I just can't remember that."
The thing is, if you make this over complicated you can come across in ways you probably don't want. The other person might think you're lying and you do remember, especially since you remember other things in that period. They might think you're making fun of them if you take it too lightly. If you're direct and honest, then it should be fine.
As far as hurt feelings go, it really depends on the other person. Some people can accept "I don't remember". Others think if they can jog your memory, you'll remember. I find that trying to jog a person's memory is just a recipe for disaster, because there's no way out that doesn't hurt the other person's feelings (if they're determined to do this).
That being said, I think trying is ideal in that situation. The event was important to the other person, enough that they really want you to remember. I would give it a try if they want to jog your memory, but if nothing comes up, be honest about that too.
Finally, if you do trust the person's memory and you want to apologize for your behavior, be as clear as possible if you're trying to apologize for something you can't remember, but don't minimize their memories or feelings on the event. Something like "I'm sorry I was rude," should suffice.
In this way you do the best you can to lessen the pain for the other person, but don't feel too bad if they are still hurt by this. If it was that important to them, it's possible that it is something that they might be hurt by regardless of how polite, courteous, and anti-pain you're trying to be. But it really isn't your fault one way or another that they're hurting in that case, and sometimes there's not much you can do. Being present and apologetic is the most you can offer in that moment.
In the end, a simple "I'm sorry, I can't remember. But I believe that it happened and I apologize for my behavior" might be enough for your situation, I think.