This question struck me shortly after waking up.
Rabbit meat is supposed to be so lean as to cause rabbit starvation. The other day, I saw a really fat bunny at the pet store. Does an obese rabbit have lean meat, just more of it?
You should definitely buy it and slaughter it to further the cause of Science. 
Rob
No idea as to the answer to your question, but on Survivorman the other night, he mentioned rabbit starvation and said that it does not happen if you eat ALL (intestines, eyeballs, etc) of the rabbit.
Here’s a thread we had on the topic a couple months ago.
But, to answer your question, if the rabbit had a lot of fat on it, I wouldn’t imagine you would have “rabbit starvation.”
Here is a good paper on the subject of high protein intake risks.
On a sign:
“Easter bunnies, live or dressed”
As stated in the other thread, the problem in rabbit starvation is that humans can’t get enough calories from only protein. If the rabbits are fat, then there’s no problem.
And I guess that the rabbit you saw was actually fat, and not some kind of bodybuilder rabbit.