We have no choice but to accept them, as Rome is the only authority to do such
I'm not sure why you keep saying Rome is the only authority to approve annulments, since I'm not saying there is any other authority that can do so. What I'm saying is that someone claiming an annulment must prove that his first marriage was invalid, and a statement from a modernist does not prove anything.
Do you have no choice but to accept the Novus Ordo too? Isn't Rome the only authority to approve a liturgy of the Mass?