don't know about 'phoning the company', but someone from the previous place might consult their linked-in profile and contact some acquaintance from the new place informally, with the aim to bad mouth their former peer. I stopped updating my linked-in profile, because this is quite possible, if you have worked in a toxic work environment (in terms of security: all what is in the realm of the possible, is also likely to happen in reality)
As a hiring manager, if someone did this, I would just feel bad for the person who was on their way to me, that they had to work with people like that.
That's a very reasonable position, on the other side: as a hiring manager you probably wouldn't work with the new hire on a day-to-day basis, and you wouldn't be involved with his performance review.
