How does this statement (by the Pope) make the Church any more open to liability concerns than it already is?
It seems to me, if anything, it would make it less vulnerable, since if no priest or bishop "owns"'their parish or dioceses, then any civil suit could never recover any financial judgement, as the persons in question never "owned" anything in the legal sense.
Legally, there is no single entity called the “Catholic Church” in the US. There is a patchwork quilt of corporations.
Some lawyer will see statements like this, and use it to say that the various legal corporations that make up the facade of the Catholic church is actually a multinational corporation headed by the Pope (There are many cases pushing that right now). In short, it means they could go after the art in the Vatican to pay for abuse settlements in say, Georgia.
There are similar situations in every church in the US that is part of a body larger than a single congregation. The corporate law is very messed up.