The adage of "where there is smoke, there is fire" seems to apply often enough with these kinds of things, and I would not be surprised if Lisa did make the assertion that she'd take VR to another network.
But, I also think Bravo plants stories with media to test the waters of possible casting and/or show changes. Assuming the gossip is true, I could see it coming from either Lisa or Bravo.
The thing about Lisa is that she is smart enough to know the legalities of what she can and can't do, but she is cunning and has a big ego. She may have thought - if even for a moment - that she could get away with it.
I am not a Lisa fan. Never have been, never will be. But, I do think she adds something to both shows that would be missed if she left. For BH, it would be the high-end luxury Beverly Hills lifestyle stuff. VR needs a central person around which all the drama can ensue. That is Lisa's role.
She grounds both shows, IMO, and is important to both.
Still, I think RHBH would survive without her.
VR will only survive if it remains part of the Bravosphere.