Well you kinda agree with me while arguing over semantics. How you wind the string and how the tuners are installed can affect stability. The tuners themselves, as long as they are not broken don't matter (ratio and slop have ZERO affect on stability, only how EASY it is to reach the desired pitch). A violin can be perfectly tuned and hold it's tuning using only friction pegs for christs sake. All a tuner is is a mechanical friction peg.
Yes, high quality tuners are nicer to use, easier to manipulate, provide easier fine adjustment, and look better. But they do NOT hold tuning any better than cheap tuners do. Tuning stability is all in the nut and studs on the JEM we are talking about here. All in the nut, studs, and saddles in a Gibson, and impossible on a strat! lol