Some of those tests can fail pure honey. Depending on the nectar harvested some honeys are lighter in colour (some almost clear) or very much darker and thickness can vary as well (can be more runny or can be very thick). Staining/marking a cloth or blotting paper…sure can and lighter honey can do it faster. Some of the staining can occur because of the pollen that can naturally be found in honey.
That’s why they couch their words very carefully with “it may” used frequently in their sentences. The jar pops on opening? Well yes it may mean fermentation it may also mean the jar has a good seal and the honey was heated slightly before filling the jar to make it flow more easily on the cold day it was bottled. Some honey has a very strong flavour that some mistake for fermentation but is the result of the nectar that the bees harvested or that it has been left for a long time in the hive before harvesting.
I have never personally tried the burning match one but I have certainly had honey catch on fire when left too long on a fire while trying to make honey caramel for popcorn. I think that test relies on the normally relative high moisture content to other solvents eg extra liquid glucose or fructose that might be used to “extend” the honey but if the honey is older, and or less moist I would imagine the match test could fail to recognise pure honey (but as I have never tested it I could be in error on that one).
I am not sure what they are testing for with the vinegar but if sucrose was added to honey it doesn’t foam, glucose or fructose is probably a similar outcome (remembering that honey has two sugars in it, those being glucose and fructose). I would expect something like a bicarb or other alkaline agent would cause the foaming but I am not sure what they would add of that nature to honey that would allow that reaction.
An old tale about the purity of honey was if it crystallised it wasn’t pure or it had gone off. But it isn’t that, it is a natural process that can even occur in the hive. Temperature, the ratio of glucose to fructose (caused by the nectars the bees are harvesting), and the presence of pollen are reasons for the glucose to crystallise out. To have a read about it https://www.wired.com/2014/03/crystalized-honey/. So another word of warning if you find glucose crystals in your honey it doesn’t mean the honey has been adulterated, it is more likely the bees that made the honey hit on flowers that produce more glucose.
But your point about honey, that it can be adulterated is well taken and yes it happens even being done by dodgy bee-keepers none of whom I am acquainted with thankfully. I can trust my producers to provide me with excellent product that every year astounds me with the variety of colours, flavours and smells that abound in them (what a wonderful thing bees produce).