So I bought a cheap "Mojave Turquoise" set in a costume jewelry setting just to test to destruction.
I am a firm believer in "You get what you pay for."
If you buy cheap, you'll get cheap in quality.
If you buy from a reputable seller or company that discloses what their stones are made from and their origins, then you are probably more likely to get good quality material.
The cheap stone that you tested was probably the cheapest stuff there is quality-wise. Mostly resin, barely spent time in a dye bath, and contained very little usable stone. Truthfully you are right with this particular sample tested - probably not even close to any real turquoise material in there - and not made with a heck of a lot of skill either by whoever put the stone together.
People say Howlite and Magnesite are the same material. Chemically they are not, though they have similar properties:
Howlite: (Ca2B5SiO9(OH)5) (Wikipedia) (Hardness 3.5)
Magnesite: MgCO3 (Wikipedia) (Hardness 3.5-4.5)
Both will take dyes and stabilization and can be cut and polished with about the same hardness. Dyed Howlite is sometimes referred to as Magnesite, which just adds to the confusion between the two stones within the gem trade.
Turquoise of course comes in a multitude of varieties and treatments.
Turquoise: CuAl6(PO4)4(OH)8·4H2O (Wikipedia) (Hardness 5-6)
Blue colors are associated with higher copper concentrations and the green colors are associated with iron impurities. Turquoise with a very light blue to almost white to it has a proportionately higher aluminum content to it.
Judging by the varying hardnesses of the stone varieties, I would think you would know which one you were using when putting it to a wheel for polishing or grinding. Like limestone, Magnesite should bubble under an acid treatment because it is a carbonate. Though since it has been dyed and stabilized it might not fizz up under the acid.
I would say the material being sold cheaply is going to be one of the softer stones. The fact it is being marketed as "Turquoise" When it contains none means you don't have a reputable seller. If they were of decent repute they would state the stone was made with howlite or magnesite that was dyed.
If you are buying from someplace like Thunderbird or from a seller that has a good reputation such as Mijo730 you are probably getting material with actual turquoise in it. Stabilized, Dyed and chemically enhanced Turquoise.
The testing you put this "cheap stone" through was informative and certainly exciting to read about. I'd like to see a piece of real turquoise and a piece of the mojave turquoise from a reputable seller go through this same test.