...which it explicitly stated it does not recognize
False. You need to learn how to read.
This phrase here --
whatever about the validity of the orders
basically means, "whatever you want to say about the validity of the orders", i.e. "say what you want about the validity of the orders", i.e., prescinding from any consideration of their validity.
In other words, the Vatican was merely referring to the fact that they're legally illicit without having done any investigation into their validity.
In some cases, the Vatican allowed Thuc priests back into "the fold" without requiring conditional ordination.