"The Vatican" dixit?

Prompted by Steve Shiffrin's most recent post, I'm finally going to pose a question that's been on (and off) my mind for more than a season.  What do you mean, Steve, when you say "the Vatican teaches" or "the Vatican says" or "the Vatican teaching on?"  Also, what do others mean when they use these and similar expressions? 

Nothing is signed "the Vatican."  What happens if we substitute the real signatories for "the Vatican?"  Does this create problems for Steve's (or others') positions on authority, obedicence, etc?