It wouldn’t logically follow for me that U.S. intelligence would disclose any information to the Vatican concerning our defense capabilities. However, I must admit my ignorance regarding the diplomatic relations between the U.S. and the Vatican. Therefore, I remain open to this possibility.

The US wouldn't reveal any capabilities. Besides the typical intelligence greed for information, all Vatican needs to know is "how seriously do we need to prepare for extra-terrestial intelligence?" I bet there are some generic contingencies in case the E.T. suddenly lands with greetings from the Galactic Federation. What the Vatican wants to know from the US (or even: what the US actively does want the Vatican to know) is "ok guys, so we actually do have a few alien prisoners and a marvellous ET starship, so get ready for a big reveal within a few decades/years/never" OR "ok guys, you'll be hearing a lot of bullshit about aliens, but don't fret, there are no aliens, these UAPs are just our own stuff and you don't need to know more than that there's no extra-terrestial factor involved."