Having dealt with a similar issue and having had my own $$$ CMM in a temp controlled workshop that could measure this, I can tell you that any or all of the above suggestions could be the case.
The CMM, if automatic and programmed properly (generally if using the OEM software then it will adjust it's speeds accordingly) and if used in a temp controlled room (well controlled, within a few degrees variation), AND if the part is heat soaked sufficiently, AND if the CMM has been also heat soaked (ie, they didn't turn the A/C off when they left the night before then ran it right when they got in that day), then it's most likely:
1) Calibration error on the probe
1a) Tip may have a flat spot(s) (these just occur over time and with rough operators)
1b) Probe may not be a scanning probe and it's measuring a tri-lobe due to inherent variation in off-axis measurement internal to the probe
1b) Probe may be a scanning probe that hasn't been calibrated or has an inherent variation issue and along with scanning at too high a linear speed for the rotation speed of the probe, may be scanning a sinusoidal-ish pattern from the probe error that's increasing the effective diameter measurement
2) Operator might be measuring something like the above mentioned inscribed circle, while if you are using ANSI Y14.5-2009 or other Y14.5, the roundness defines a complete profile and no point may exit the high or low profile. Inscribed circle will always capture the peaks, not valleys. It won't capture point failure.
3) Somehow you have always measured in low spots with the mic and your average is trending lower than the true average
4) Your part may be at a lower temperature when measured than when the CMM is measured. BTW I assume you specified a temperature for the part dimension to be measured at. Your functional requirement temperature is one thing, but the part dimension for inspection must be that at the Q/A facility room temp and pressure. If you're facility colder, you will measure smaller.
We had a 2µm repeatable accuracy on our CMM and Renishaw scanning probes consistently measured a 1.5µm lobing on sub-micron round parts due to the probe design. We repeatedly had the CMM company calibrate the CMM, but they don't calibrate by scanning, just by touching 3 points to get a circle. The probe would rotate the tip in each spot for an averaged location, which eliminated the tri-lobe error perfectly. The issue was that when you scan, the CMM doesn't stop and perform at least a 120° rotation at each point, it is maintaining a continuous travel to avoid introducing vibration and rolling the tip along the surface to reduce tip wear. The downside of saving a few bucks on replacing tips every few weeks and getting higher CMM throughput is that you would get the weird sinusoidal measurement from rolling the tri-lobe error onto the surfaces. On runout measurements you got this interesting soft peaks and valleys measurement at the micron level, that looked like you were measuring surface roughness, when actually you were measuring the Renishaw design flaw.
This was years ago, I hope they've since solved this, but the probes are $$$ so I imagine a great many of these are out there.
Good luck, dealing with this level of accuracy in a Q/A dispute often leaves no winners.