I think one of the issues can be that let's say you think you have a certain condition. You read about it online, and think "oh yes, that's me" for some of the symptoms. There's a few you hadn't thought about before, so you start looking out for it and convince yourself you do have those symptoms.
That's not a new phenomenon, I think it's the "Doctor in the House" (by Richard Gordon, written in the 50s) books, where the doctor reads through his book of illnesses and concludes he has everything in it except housemaid's knee.
But it's the first generation where people can easily go online and find out the symptoms.
Also, no one ever does a blog about "I had this symptom and it turned out to be nothing" it's always "I had this symptom and it turned out to be the 1 in a million chance it was something nasty". So people get a disproportionate idea on how likely these things are.
So, yes, I'd say that people can go to a doctor thinking they have something and convince them, but I'm not sure it's deliberate. More, they've thought they have it, and their brain is convincing them the more they read.