After reading the TSB on refinishing 6MT brake discs, would nondealer brake shops have the same type of equipment to conduct "on car lathe" refinishing?

This is a required method as stated in the TSB.

 

I could be wrong, but isn't this a fancy term for "turning" or "resurfacing" the rotors - a necessary step in ANY BRAKE JOB!! I think this "on car lathe" is simply a machine that doesn't require the added step of removing the rotors to be resurfaced. Instead, it does it while the rotors are on the car.

Could you post a link the the TSB?

 

http://www.in.honda.com/Rjanisis/pubs/SB/B04-019.PDF

http://www.in.honda.com/Rjanisis/pubs/SB/B00-037.PDF

also can be found here:
https://acurazine.com/forums/showthread.php?t=154245

 

the on car system is a specialty tool- call each shop and ask if they have one

It cuts the rotors straight with the hub as it rotates under engine power-
not just smoothing it to its own rotation- making it a unit with the driveline

result is smoother braking in cars with known touchy rotors