Like I said, that diplomacy screen is a bit confusing in the way it's worded. Maybe they did become MY vassal. In any case my assumption was it would not last, but it was a handy breather for me since I did have a war going with Milan too.

It started as an offer to me though. Even though they were being crushed rather soundly. Maybe they were offering to become my vassal, but it didn't read that way at the time.