I don't think NOT having a facebook account has ever prevented anyone from getting a job. Rather the opposite, actually.
Well, you're wrong. I've had interviewers ask why I host my own blog instead of using Facebook, and said it was very unusual that they couldn't check out my social background.
And Craiglist rental ads often screen applicants using social media, usually Facebook.
Well, why would an employer need to check your social background? They should care about your skills more than anything else.
Thus said, a call to previous employers should do the trick.
Personally I'm on no social network, on purpose. I've never had any issues. If it was an issue for an employer that I didn't have a Facebook account that their issue not mine.
I don’t know what it’s like where you are (or what it’s like where I am now), but in the U.K. references from a previous employer are limited to confirming that a person worked at a place between specific dates.
This is because everyone gets legal advice warning they may be sued for libel if they either say anything negative or have a policy of saying nothing only for bad employees.
I don’t know how likely the scenario is, but everywhere I’ve worked before I left the U.K. shared that policy and that reasons.
I don’t want to work in an office with an unrepentant violent criminal or vigorous racist. Irrespective of their skill.