The providers that I've been to are way too busy to look people up on the internet..

I worked with a psychiatrist who used to do it to clients whom he felt were lying to him, stealing from him or hiding his stuff.

It would be creepy to know that a therapist looks up a patient for no reason. Just like many therapists would feel uncomfortable with that happening to them. They may not say it to the patient, but I'm sure they feel uncomfortable. After all, they are human and want their privacy.