I don't think anybody would ever call a current employer, that'd be so stupid on so many levels. Moreover, if they really want, they can probably find who you work for anyway, no?
Years ago some idiot recruiter approached me by phone at my work. He got thru chain of offices and people to reach me by my name. As I had no phone on my desk finally my manager passed me the phone to answer the guy in a room of four co-workers.
I wasn't looking for a job that time actively. Possibly my name and company name on LikedIn was enough for his desperate quest.
"Two things are infinite: the universe and human stupidity", A.Einstein.
"Two things are infinite: the universe and human stupidity", A.Einstein.