I don't know for the US, but in Europe fake honey is a big problem. There were several grocery chains who had to call back their honey because of it
https://kinghavenfarms.com/blogs/from-the-hive/the-sticky-bu...
For a low tech pure honey detection you can mix a few drops of honey with a warm water then swirl the mixture in a bowl. If you see the appearance of seamless hexagonal pattern appearing like a honeycomb, the honey is said to be pure.
I've used this method many times and mostly works, i.e the hexagonal honeycomb pattern does appear, but the honeycomb pattern probably can appear with fake honey as well. It will be very interesting to test this rudimentary technique with fake honey for accuracy.