Exactly. A good portion of people appearing in episodes of the MTV show Catfish do not have non-phone computers, and carry on their fake relationships via Facebook, Twitter, SMS, and sometimes voice calls. It often takes only seconds for the two guys running the docu-drama reality show to determine that the victim of the week is being conned, and image search and reverse phone number lookups are always the first two things they do.
It would have to be something that social media companies or telecoms would do, on the same order of difficulty as poking a button on your iPhone app, or dialing a phone service code like *57.