You are approaching it from a rational viewpoint. You can't do that. Remember John Hinkley? Rebecca Schaeffer? Both stalkers were convinced they had relationships with the actresses. They see interactions by delusionally interpreting what the celebrity says and does. They read in secret messages to them from the celebrity. The relationship is completely real to them.
I don't think someone could feel they have a relationship with an artist don't meet personally, although he's over obssesed. Because of the definition of relationship, there's no relation.
But, anyway, here with models there's contact and kind of realationships occurs, so that's why I concluded with this:
Here is a question for users that are confused with feelings with models:
Do you think you would have had the same story with the girl if you hadn't paid?
For op: ask yourself that question, think about it.