I'm not 100% sure on this one since you can't smell it but I will post this anyways as something to consider.
It's a longer post sorry but if you rule everything else out this could be a possibility.
The smell could be from anal glands however it is pretty noticeable so I'm not sure you could miss it. Either way this is one topic in vet medicine that we all know about but seems to be virtually unheard of in human medicine. So here's a rundown of what anal glands are, what they do and why they stink.
Mammals have anal glands or anal sacs, including humans. Humans have 7 to 14 different glands. They fill with a foul smelling fluid, usually described as fishy poop smell, that is usually expressed naturally when we poop. If this doesn't happen they can become too full. Have you ever seen a dog scoot on its butt? It is trying to express the anal glands. In humans we can't do that, and have to wait for our body to do it. It can make pooping painful for what seems to be no real reason.
As far as controlling them, no animal, including humans, can control it. Some animals will express their anal glands when they are stressed by a situation, suffering from anxiety or scared. It is a reaction for defense and nothing you can do to stop it. For example, if I'm restraining a dog that is extremely upset it may express its anal glands. The most famous example though would be a skunk. Yep, same thing! When skunks spray they are releasing their anal glands. Even in skunks that is not controllable. It is a fear reaction which is why those raised with humans and other animals don't do it -
they are not afraid. When possums play dead they release their anal glands to help the illusion. Even though it is normally a fight or flight response sometimes the body will just do it when there is no stressed. Skunks and ferrets commonly have them removed in the pet trade but that is becoming a banned procedure in many places. I believe in humans they are located further up and much harder to get to. I have not found any information on anal gland removal in humans. I would assume if one abscessed it could be removed other than that in not sure.
As far as expressing them that can be done in some animals. In a vet clinic if you can put your finger in its butt they can be manually expressed - most commonly we express canine anal glands. Sometimes cats but that is an uncommon problem for them. In the event that they are not expressed they can become infected and even abscess. This happens in people too, it is the cause of an anal fistula. I believe in people the glands are not easy to get to like they are in small mammals so I do not know if it can be done in people.
When anal glands express you wouldn't necessarily feel anything, there usually is no sound like a fart. It is fluid tho so you could feel wetness or actually leakage. Theoretically stressing about it happening could make the problem worse. Although sometimes stress can have nothing to do with it and the glands will release for seemingly no reason. In small animals we don't see that as often but it does happen. Constipation or chronic diarrhea can make this issue worse because the glands are not properly able to empty. Just something to think about.