Machine shop refuses to install exhaust valve seats

In the right hands a telescoping gauge is accurate
same as the dial bore gauge. In the wrong hands neither is worth anything. Taking measurements is an aquired feel or skill.
The dial bore gauge is more expensive and purchased for gathering measurements faster.
It is really the machinist's choice as far as which tool he feels he gets the best measurements with.
Good micrometers are very accurate I wouldn't
call him an idiot because he wasn't using an expensive snap gauge for efficiency.
Not saying the guy should be building a performance
engine but there is more than one tool for the job.
One no better than the other. If you are careful about
choosing your machinist he will know what tools he needs to be using.