A comment about the touchstone the guy used.
What that guy on the video and most everyone else don't seem to realize is that the touchstone test is a "comparison" test and not a test where just using the acids alone automatically tell you what you have. The way to correctly use the touchstone is to compare the reaction, the reaction time, and the reaction colors to samples of karat golds with known karat compositions. You make streaks side-by-side of the standards next to the unknowns, apply the acids to all, and then immediately observe and compare, for about 10 seconds, or so. The more standards you have, the more accurately you can narrow in on the true karat of the unknowns. I read an article about the British Assay office that said they could use the touchstone with an accuracy of 1/4K - about 1%. They must have had a ton of different standards. I don't know what they presently use there, but I wouldn't be surprised if they still use a touchstone.
Please note that you can't buy, for example, 13K or 15.5K acids. The standard 10K, 14K, and 18K acids will work for all the karats in between, as long as you have standard karat golds to compare.
The 14K, and higher, acids are some form of aqua regia and they will slowly lose their strength over time. They can also get contaminated. Therefore, the reaction on, say, 14K yellow, will change over time. However, by comparing the sample against standards, this change will occur on both, equally.
After spending a lot of time with the touchstone, since they have developed a good feeling for the reaction times and the colors produced, a person might dispense with the standards. However, standards should still be used often to check if anything has changed. A place I once worked for bought and liquidated an old pawn shop that had 1000s of rings and other items which had to sorted by karat. I soon was able to sort them with decent accuracy while occasionally using standards.
When buying, I prefer the touchstone, any day.
It was interesting that the x-ray came up exactly 14K on both pieces. Why not 13.8 or 13.3, both of which being much more likely?