That is the difference between CMM and gage pins: fit. You can not have line-to-line fit - that is called press fit, and the pin will never come out. So, if a 15.88 pin goes in, the hole is already too big.
On top of fit, pins measure MMC. So, a CMM will find diameters even larger based on roundness.
The only way it works out is of the customer agrees to that measurement technique - then you are on the same page and all is well (until they get a new quality engineer.)