Nope. No matter how good your intuition may be, you're likely not getting a complete picture of the person based on their online persona, even if you can correctly apply the diagnostic criteria. That's not to say it's impossible. It just isn't responsible. There are labels and stigma associated with diagnoses that can have a really powerful effect on people inasmuch as how they perceive themselves, and how others perceive them.
Aside from this, I think it's important that someone who is actually diagnosing has dealt with a variety of mental illnesses and had related supervision. That doesn't make their decisions infallible by any means, but I'd personally be more trusting of someone who's put in a lot of time piecing together relevant information through direct in-person interaction than someone whose entire experience is via classrooms, google, or other media. Psychology, clinical social work, and MFT internships tend to build this experience into higher learning and subsequent employment.
Thank you for bringing them to light. I've often wondered if my sharing information is obtrusive or indeed helpful when a person solicites it from me. Often sharing well wishes and the tag line "in the end, only you know what you need and what is best for you". I believe in this way perhaps the person may find value in my knowledge of a thing, or at best look for their own answers from more a credible source. All-in-all I try to ensure they are treated respectfully. 
