IANAL, but can they really do that? My only direct experience personally is a Visa that I had about 15 years ago where the issuing bank was bought out by Citi. Citi converted the card to an Amex but transferred over the balance, payment history etc. Something like that seems more likely, or what they have been doing in prior years of watering down the benefits and jacking up the AF on the legacy cards to "encourage" the cardholders to switch to a different product or walk away altogether.
I think as a business/contract matter they can, although I imagine they view it as much better to try to convert you to a different product or reduce the benefits and get you to cancel.