I'd like to think that because of the instrument - professional pianists probably can sing better in tune than those who don't. They may not have a great voice, but their tuning is probably pretty good.
Although, I have perfect pitch so I'm biased. 
Yeah, you have to explain this more. Pianists have a couple things working against them. They don't have to use their ears to listening for tuning (/can't adjust the pitch), so it's not something they're focusing on. And the piano itself, even when tuned, is equal temperament, so pianists aren't hearing things as in tune as they can be.
I've got my own ears/experience as an example on the crappy side (although I've worked to improve that). I also remember meeting a pro pianist who couldn't really tell flat or sharpness between two pitches. That guy had perfect pitch so he knew the notes but he didn't know which was x-cents higher or lower or which instrument needed to adjust.
Vocalists and esp. string players though... Look out.
It depends who the person is that we're comparing a pianist to also. If you take a pianist with basic ear training vs. someone who's never sung, the pianist would win out most likely I would think. The other person has never used their voice or their ears much. There would be the except of the person who just hears or sings better though.
I never considered a piano that helpful for tuning. Even for ear training it's just giving you the pitches. It's limiting the musician that way. Actually using the voice/ears or a string with the ears, definitely pushes the issue/forces the issue of having to adjust that pitch. I've thought something electronic might work, but haven't run across something that's as easy as a string or the voice to slide along to adjust pitch.
Trombonists too... They tend to have good minute tuning abilities since they can very easily do that kind of adjusting. I suppose lower pitched instruments in general would have good basic interval hopping tuning ability since they would get reamed more by the conductor for doing something like moving a fifth or fourth without being very in tune. They can throw the rest of the ensemble off.