I can’t speak for KSU, but I think you may be pushing your position a bit too hard. There may be some good reasons for KSU to adopt the position taken.
Regarding “suspicion,” “evidence,” and “accusation,” let’s look at those terms forensically. If the police suspect that some one has committed a bank robbery, and, upon searching that person’s belongings, they find large amounts of cash in a duffle bag, that cash would serve as “evidence” to a possible crime. They may think it proper to “accuse” that person of the crime, but they would not do so formally unless and until that evidence had been examined and the context for which that person came into possession of the cash was explored.
Now, in using this example, I’m not suggesting that the Vatican is committing anything “nefarious.” I’m merely looking at the terms being used. And I am certainly not making any accusations against the Church. I am suggesting, however, that there may be “evidence” indicating that there may be some political shenanigans coming out of the VPO that are worthy of further examination. Such a surmise is, of course, speculative, but, given the history of the Vatican over the centuries (and perhaps in recent time), it is not improper for the faithful to monitor the functionaries and functions of the institutional church in Rome.
Finally, I seriously doubt that (using your words) "the Church (is trying) to twist Church teaching to impact US politics." The Church has bigger fish to fry than coercing the US government. But, would some elements who have certain agendas within the organization which is the Vatican want to influence the Church in general? You bet they would.