Learn English – A word for teasing someone with information they desire

If the question is what to call the "behavior" of a nag or naysayer, I would suggest "hyper-critical" to be downright literal, but I would also consider calling this type "oppressive" in the sense that they weigh you down psychologically, or "overbearing" in the sense that they violate your comfort zone to criticize you.

It's called cyberchondriasis - combination of cyber and hypochondriasis.

http://www.ncbi.nlm.nih.gov/pubmed/22137465

A type of hypochondriasis that develops in a person who, while on the Internet, identifies one or more personal symptoms—e.g., tachycardia, dyspnea—and ties that to one or more conditions; the individual then convinces himself/herself that he/she is suffering from these conditions (freedictionary).