I will concede that to get an accurate absolute measurement that you need controlled conditions. Most of the measurement that is done in the shop and especially the home shop are comparative. So let's say I need to fit a bearing to a bore with a light press fit. The bearing measures 2.2504, and I want a 0.0005 interference fit. Then I'm going to make the bore 2.2499 as measured with the same tools and ambient conditions. This is not an absolute measurement but a comparative one. With care and experience, it's pretty easy to hold +/- 0.0001 or better when machining.
With practice, it is easy to get a repeatable measurement to 0.0001, even when transferring from a snap gauge or an inside mic. But again, these are not absolute measurements, close but not exact as compared to a traceable standard. It's all about feel and as you say, your senses.