Can a volume of gas be measured by change in PSI?
Volume is inversely proportional to pressure only when:

1) the number of moles of gas is held constant. We can say this is true in your situation because the repairman measured the pressure in the tank and I don’t think a significant amount of gas disappeared from the tank in the time it took for him to measure the pressure.

2) The temperature is held constant. Again, I don’t think temperature dropped 20 kelvin in the time it took for him to measure the pressure in the tank. 

This follows from the ideal gas law equation – a good approximation most of the time:

$PV=nRT$.

So I say your repairman still has his wits about him and isn’t trying to rip anyone off.