Can facebook give out ip addresses?

Unfortunately I work with some really immature kids who thought it would be ok to spread lies and slander about me, and compromise my job. One of them claims someone created a fake facebook account and emailed his girlfriend to say he was flirting with a colleague. They have since split up and he is obviously set on revenge. Let me just start by saying I actually have a life, and was not even aware of this situation until a few hours ago. Life at work has been a living hell the past few weeks and now I'm aware of why, I will be going into work tomorrow and filing a complaint, but first I want to know if he is lying about contacting facebook and asking if the IP address of the fake account matched anyone on his friends' list - in this case, me - or if they are legally allowed to do that? My computer-savvy friend says as I use facebook on my phone the IP address will be the same as anyone else using that network signal, whilst others say facebook are not allowed to give out people's IP addresses like that. Does anyone know what could be the cause of this because I'm certainly not pathetic enough to get involved in petty drama that could cost me the job I worked so hard for. Thanks in advance.