The company will only verify dates of employment. It's Equifax and is called The Work Number, and you can see it in the elink section where the W2 info is kept. (Payroll locked this down after the Equifax breach.)
That said, there are ways to work around this...
If you are surplused, or think you will be, make hard and soft copies of your A&Ds or annual reviews. (You should do that anyway so you can join the inevitable age discrimination lawsuits or refute unemployment denials.)
Contact all clients, coworkers, or supervisors who are willing to act as a personal reference for you... If it's their personal opinion, and they state that, and any reference calls are done on a personal cel or personal line, I don't see why the company would have any control over that.