"If you use software licensed under Facebook's BSD + Patents license, and the author of the software (Facebook) has patented technology in the software (which AFAIK they don't), the author CANNOT sue you."
This is just flat out false, and i'm not sure why you believe this. The termination is broader than the grant. The grant is for patents in a given piece of software, the termination crosses all software.
Concretely: if you use react, and they sue you over patents in notreact, and you countersue, you do not lose your react patent license. They are still welcome to sue you over notreact, there is nothing in this license that will prevent that from happening. It only gave you patent rights to react.
(It also says that if you sue them over notreact, you will lose all patent licenses in all software that use this license, which is why the termination is broader than the grant).
"The BSD + Patents license is strictly better than the regular BSD/MIT licenses. You lose no rights, you may gain some patent protection."
This is also an incorrect legal statement.
Once their is an explicit grant, any implicit grant you would have gotten is extinguished. In this case, the terms of the implied grant were much better for people than the terms of the explicit one. So you are, in fact, losing something