Personally I would say that almost any zoo animal, only under the supervision of that specific animal's keeper. You might be an expert in a species but it is the keeper that is the expert in the individual. I wouldn't even pet a dog without permission from the owner!
Absolutely hit the nail on the head!
I prefer to allow people see me make contact with animals that I personally know will be amenable to it. It gives them the opportunity to see another side to these animals (in my case herps, often seen as robotic!), rather than giving them the message that it's ok for them to violate the animal's space for their own pleasure.
The animals I work with are not forced on display, nor are they housed in a way that allows them to be touched by anyone without keeper access. These animals are not goats in a petting zoo, but for some of them a measured level of contact between them and a trusted keeper may be beneficial in many ways.
Of all of the species I work with, the only ones that get "petted" are;
Radiated tortoises - these animals respond to a particular touch on the forelegs and "present" by standing up on tiptoes and allowing their legs, head, neck and recesses to be examined, the payment is a tickle in the soft skin of the shoulder, they love it.
Lesser antillean iguanas - We have 6 of these, all but one were territorial aggressive and contact intolerant when I arrived. Gentle work over time has made all 6 contactable on their terms (if they're not in the mood they simply aren't in the mood). I make contact with each of these animals every single time I enter their enclosures, reinforcing my association with neutral or positive things, it's genuinely enjoyable to do this in view of many many people, hear the pleasure and suprise experienced by the viewers, then step out to explain the benefits of this to the animal. Usually coupled with a cheeky comment of how it is pretty cool for me too, maintains the mysterious and impressive status of the "keeper".
West indian rock iguana - The now lone female we have is worked with according to time periods of the day. First thing in the morning she is contactable and "catlike" in her enjoyment of it, this opportunity to help out with loose shed skin etc, grooming reinforces a good relationship. After the basking spots come on at 9:30, she's in food mode till midday! No petting can occur when food is being delivered, I also provide a D3 supplement weekly in two pieces of banana, again, she will sprint and jump 3' up for this, a strict protocol is required. After midday it is possible to go on the enclosure on a different routine to change drosophila jars hidden around the enclosure that provide food for whistling frogs, again a different response, she comes over inquisitively at this point and actively seeks a tickle, contact relaxes her and effectively stalls her, meaning I can get away with bending over in awkward places without getting jumped on or bitten by her.
The most important aspect is that each of these things are necessary and there is never petting for petting's sake. I really do feel that where appropriate it is best presented by keepers themselves to stave off people's interest in doing the same themselves without the understanding of the animal that you explain to them afterwards.
I'll admit to being incensed when I discovered a member of the public almost over a tortoise paddock fence in order to pet a female radiated tortoise who was infact laying at the time!!! That animal abandoned her nesting attempt that she had spent half the afternoon making and was disturbed from a usually straightforward laying routine for a few days afterwards.
Musing.
If you don't know the animal why would you take the risk, why would you snatch a quick stroke despite the fact the animal might react badly, sure once it's reacted badly you'll stop, but you've still gotten what you wanted and that animal is still left disturbed as you walk away glad you kept your fingers and got away with it. They might enjoy it true and in that case, well how lucky!
But you don't go for a walk in the forest with any expectation of being able to pet the badgers, foxes, squirrels, hedgehogs etc lurking in there somewhere, the only reason zoo animals might be subjected to this self indulgence is because they're fenced in!
I'm not really sure how I feel on sneaking a stroke of an Eland or whatever else sleeping against a fence, only to say that I've never done anything like it at any zoo that I've ever visited.
