I'm not even sure the Space Shuttle was built with those ridiculous tolerances. Maybe some internal engine parts like turbopump rotors and shafts. Does he know what he's saying?
10 micron (0.01mm) is pretty reasonable tolerance for a lot of stuff. The laminations in Tesla's motors will be held to somewhere around that, possibly even tighter. Things like motor winding insulation coatings will be far tighter.
For something like body panels or plastic interior pieces it's utter overkill and a waste of resources.
Something like a body panel is going to expand/contract a couple of orders of magnitude more than 10 microns just from the weather changing day-to-day.
It's pretty common for a CMM to be in its own climate controlled room. Parts will be placed in the room and allowed to reach reference temperature for a several hours prior to measurement.
On production lines you usually skip the absolute measurement of a CMM and use go/no-go gauges. One should fit, one should not. They'll be made of a material with similar thermal expansion coefficients as your parts. As long as they've both been sitting around for a while they'll be at the same temp. They'll have expanded or contracted the same amount from reference so their relationship of go/no-go will still hold true.
The whole field of metrology is a never ending rabbit hole - really interesting the more you get into it.