Hmmm... Fairydoll, I've already given input in this thread. But I guess you mean specifically on the domestic abuse issue.
Fortunately, I don't have any personal experience with it. But I think the professor may be referring to a Restraining Order (RO). I've heard (read maybe?) that you can get one without proof - you have to give a reason, I think, but don't have to prove it cuz not all abuse leaves marks and so forth. Usually - I think - the RO would include the kids, too. So yes, I guess a woman could make a false claim and so keep dad from kids. Or it might just mean limited, supervised visitation - I'm not sure. (Sorry I'm not much help here.) But I hope false charges are few and far between.
But ladies, not all cases of EGPs are about "abuse" as many of us think of it. I've heard of ones that are "just" about repeated offenses, last straw situations and/or continual disrespect. If parents ask a GP, for example, not to give their kids sugar and the GP keeps doing it, and the parents remind them and explain, but they argue/brush it off and just keep doing it, after a while, the parents are likely to cut back visits or even stop them altogether. Then the GP might complain, "They cut me off just because I gave my GC a cookie!" But it really was cuz of a string of offenses, culminating in the cookie incident.
Or it might occur due to a zillion little things - some people call it "death by a thousand paper cuts!"
I'm NOT saying that any of this is the case with any EGPs here. Just saying that it's not always about abuse per se though in its own way, it may be just as understandable.