Everyone seems to have a different read on what is best. Had some shipped with a bunch of perlite in the bag recently, that was a new one. Had some delivered with coco coir as well. I can understand why someone would want to put paper towels in and I don't blame them, but there is really not any standard method. Even professional scion sources like Fruitwood nursery send in wet paper towel. I don't complain with however people send them because I am just stoked to get something new in general, but I'll ask them to not send wet paper towel on the second order if I remember to.
My experience has been that most scions can survive on the counter (dry) for almost a week if they're bagged, even 10 days sometimes, but I always squeeze out the air like Brad says. If they're buddytaped and bagged I'd guess even longer. If they're wrapped in wet paper towel, you could see mould start to form in less than 2-3 days depending on temperatures and if the scion has it on the surface. I don't have much experience with the fridge but I left some cherry scions in there recently for a month + and they still look totally viable. This seems especially true for wood that is dormant like figs or stonrefruit but I think jabo and eugenia you need the freshest possible.
I also like receiving untrimmed scions with leaves and the little green fresh branches and then I get to make decisions about their shape and size. I note that Y shaped branches often do really, really well for some reason. My thoughts are that the wood will pull moisture from the leaves, but then I guess there is more chance of sending invasive bugs or fungal stuff that way.
It can get even more deep: I try to cut them in the afternoon right when the sun is about to set, I figure maybe they're kind of "charged" from the sun but that's a kind of bro science thought process, had just read about it somewhere in my grafting research.