no_biz---I know you're a regular CZ poster and from reading your posts, it's easy to see that you care about your daughter. With that said, you are obviously concerned about her very frequent self-gratification or you wouldn't have asked for advice. Some time ago, you mentioned that you have a telepathic connection to your daughter thus I believe that on a gut level you sense something isn't right. If so, please listen to your gut!
I'm not saying that your daughter was molested but there is obviously something troubling her. If you looked at the link I posted for you, you saw that if something is troubling a child, it could cause him/her to excessively spank the monkey.
You raised some red flags with the "Anna" story your daughter told you and with the fact that she tried to get you to touch her. IMO, you need to get to the bottom of this. Maybe "Anna" is a figment of your daughter's imagination--does she have a vivid imagination? If so, asking her about "Anna" will help you to sort fact from fiction. Or maybe "Anna" is real. You could start the conversation by asking your daughter about preschool. What did she like about it? What didn't she like? Which kids did she like best? Once again, remind her that she won't get into trouble and can tell you anything.
Whatever the outcome of the "Anna"/preschool situation is, you should still have her checked by her pediatrician. Have a private discussion with the pediatrician before he/she sees your daughter.
Yes, self-gratification is common among preschoolers and by not making a big deal about it, you are doing the right thing. I remember my daughter when she was not quite 2 years old one day when I changed her diaper. Upon opening the diaper, she took her hand and started squeezing herself. She smiled at me, I smiled back, when she was done, I completed the diaper change. However, never once did she take my hand and try to get me to touch her in that way--not during that diaper change or at any other time.
If something is upsetting your daughter--no matter what it is--please find out what's going on. In the end, you will be glad that you did so.