Both tires, and rims, vary quite a bit more, among brands, than you might think. Not individual units, but specific types of rims hold to specs a bit more or less than others, and tires vary at the bead and heigth and width as well. It is quite possible that some 2.8 tires fit quite well, and some are just a bit too loose.
When you push the edge of the envelope, sometimes it does not work out well.
Also could be clearance issues in addition to falling off the rim type problems.
1st off, let me say IDK anything about the Averton, but you should assume the company knows the product they sell... or maybe not buy one. I saw a couple of them the other day while riding. https://photos.app.goo.gl/rr9poQHdZ1cbC8Gb7 The couple were in their 50s maybe... late, late 50s, but the older I get the less important that seems. They were brand new with less than 100 miles on them. Before I give my opinion of the bikes, ah, do you own one, or are you thinking about buying one? One thing I will say is that if you look at the front tire you can see it's going to be "unfun" hanging fenders on one of them. Maybe the company designed some cute proprietary skin that screws into the fork, but you aren't going to fit one between the tire and the fork crown. If you did road debris and leaves would be sticking in there all the time. The tread on those tires might make some interesting noise. If those are good high-pressure tires they look perfect for that bike. The husband stood with me talking about my bike for 20 mins until his wife started giving him the stink eye. I think I sold him on a dynamo hub.
My rear rim came with a 28mm tire. I put on a 38mm, it was tight, had to grind of a bit of frame and brake mount. Replaced it with another, absolutely no go, inflated tire totally locked to the frame, no clearance, did a bit more grinding, no way. Much different tire. Went down to a 35mm, HUGE amount of clearance. A 38mm of the same "profile" as the 35 would fit no problem. The "profile", not sure if there is a better word, exact height and width, is what will vary. If you go oversize, make sure it is a wire-beaded tire. Tried one of the other kind on same rim, did not end well at all. Funny story.