. . . I've seen two identical Starrets compared to a Millennium Series Limited Edition Mitutoyo.
Even though one Starret has been used a lot and the other one almost never used, they read very close.
The brand new Mitutoyo is about .0005 less on a standard. . . . .
If either a micrometer or a caliper reads .0005" less than the standard, the response is to calibrate the tool. Might even be that the OP's ISO manual, like most, has a procedure for routinely calibrating instruments -- and would either re-calibrate or take a tool out of service that didn't meet spec.
It's quite common, for both 0-1" micrometers and 0-X" calipers to show discrepancies between their closed "zero" position and measurements further out. That's why mic checking standard sets use a variety of gages, to catch different rotations. Ideally, one uses a standard (with both micrometers and calipers) that's close to the measured dimension. This won't turn calipers (or most micrometers) into .0001" accurate instruments (the 10x rule of thumb for instrument accuracy vs. inspection tolerance) -- but as Milland said it should help remove some sources of error.
Personally, I think the OP's bigger problem is that he's been hired to be the expert at his job - but his new company clearly doesn't think he's worth listening to. He can either work to gain the needed respect and understanding (turning the company into some mythical ISO police force isn't the answer) or find another workplace that values his input.
In this case, could be he's right -- that a part being, say, +/- .0018, rather than +/-.001 would catastrophic for the customer. If so, bravo for keeping the customer's needs in mind. They pay all our bills. Could also be that he's making a mountain out of a molehill?
The QC guy most companies want will find a way to measure the desired accuracy quickly and cheaply - and even help pinpoint and solve process capability problems should they become an issue.