I'll change my initial comment into a real answer.
The human digestive tract has evolved to allow us to be broadly omnivorous, safely consuming a wide range of vegetable, animal, and mineral-based foods. While honey can be damaging to exposed cells, the epithelial cells lining the digestive tract are not exposed like the endothelial cells that line the circulatory system. Eating honey is not the same as injecting it into your veins.
A layer of mucous covers the cells of the digestive tract from mouth to colon and provides both lubrication as well as protection to the cells underneath it. It is protective to varying degrees against such challenges as acid, osmotic stress, mechanical damage, and foreign microorganisms. Additionally, the cells themselves are layered and are continually being sloughed off and regenerated, so even if the mucosal lining isn't 100% effective, damaged cells will be replaced fairly quickly.
Food quickly travels from the mouth through the esophagus to the stomach, not allowing enough time for osmotic stress or enzymes to damage anything to any significant degree. (Obviously, if you swallow something extremely harsh like bleach, lye, or concentrated acid, that's a different story.)
Once in the stomach, a food like honey is diluted by the digestive juices and any other food or drink already present -- it's not like the stomach is totally empty and globs of honey can just sit in direct contact with cells for an extended period of time, allowing for osmotic or enzymatic damage. Digestive enzymes and the acidic environment quickly attack proteins and other substrates, so even if the glucose oxidase can become activated, it will be cleaved by proteases into inactive fragments long before damaging levels of H2O2 can build up.
Low-density lipoprotein (LDL) is found in the bloodstream, not in the digestive tract, so any methylglyoxal present in food would need to be actively transported into the blood to do any damage. The work in the paper you cited was done completely in vitro, with no evidence that MG-mediated glycation as a result of eating honey actually occurs in people.
Many foods we commonly eat would appear to be dangerous to our bodies in one way or another, yet we have evolved strong mechanisms to minimize harm. However, it's pretty clear that some foods are damaging in various ways over time, so we still need to moderate what we eat. I don't know if honey (or certain kinds of it) is one of those foods, so more research is needed.