I should add that if a bunny looks like they are very unhappy and possibly not going to eat/poo/wee then I'd speak to the owner.
I actually go over the owners rabbits normal behaviour before they are left with me so that I know if they aren't terribly happy.
I have had one bunny who came to me for bonding (with the owners other rabbit) who was immediately not how I'd want a rabbit to be - not interested in eating hay, sitting quietly, laclustre, so I sought her input and then had a look at his teeth. Sadly his teeth were not in good shape and he couldn't eat properly. He had a trip immediately to the vet who sought the ladies consent to do a dental - her expense not mine.
Sadly on this occasion the bonding didn't go ahead, but the bunny was poorly already.
Not quite the same thing as the rescue being involved, but similar in that the owner could have suggested to me that the bunny was ill due to my attempt to bond.
Your question is a very good one, and I think it has made me think about how a rescue should seek volunteer help to do bondings too - at what point does someone become experienced enough to do bondings for other people? You have to do bondings to get experience, you have to start somewhere.