Regarding plastic tools, yes indeed. I have never aligned a tuner but have done a tape deck and metal tools do indeed affect the measurements (at least when the adjusters, eg. trim-pots, are also metal).
Regarding tuner alignment, why is it such a black art that nobody is willing to reveal??? Never mind warnings of us students potentially ruining our tuners -- that's our problem. People just don't seem to want to explain it, the information doesn't seem (to me) to be available on the 'net and it seems to me this "art" is going disappear unrecorded into history and be taken to the grave with the seemingly few who know about it.