Measurement is where arguments start
Why two parties measuring the same part reach different conclusions.
Two parties measuring the same part reach different conclusions because "the part measures such-and-such" is never a complete statement on its own, and unless both sides have agreed on the same instrument, technique, calibration standard and environmental conditions, each is honestly reporting a different measurement while believing they are reporting the same fact about the same object.
Two tapes and a wardrobe
Two people arguing about whether a wardrobe will fit through a doorway, one having measured the opening with a stiff metal tape pulled taut and locked, the other with a soft fabric tape that stretched slightly under the same pull, can both report a careful, confident number and still disagree. Each is certain, and from where each stands, each is right. The argument is really about which tape, held which way, deserves trust, a question neither thought to settle before measuring. A fabric tape stretched a few extra millimetres looks no different to the eye, its markings crisp either way, so the disagreement rarely gets traced to the tape until the two are laid side by side under an identical pull.
A customer and a supplier disputing whether a delivered part meets its drawing are usually having the same argument at a smaller scale. Every source of drift earlier in this set, repeat scatter, resolution mistaken for accuracy, a caliper's technique-dependent errors, is still present when two people in two places each measure their own copy of the part. Neither needs to be careless for the numbers to differ, because the two processes were never verified to be equivalent.
The part that grows over lunch
Metal expands as it warms, and precision measurement is referenced to a standard temperature of 20 °C for exactly this reason. Steel grows by about eleven thousandths of a millimetre per 100 mm for every ten degrees, so a 100 mm steel part carried from a cold morning floor into a warm afternoon inspection room ten degrees hotter can grow by more than a hundredth of a millimetre, the entire width of a tight tolerance band. Aluminium moves about twice as much. The honest answer to "does this part meet spec" can flip within a day while nothing about the part or either side's technique has changed.
A steel gauge checking an aluminium part compounds the effect, since the gauge and the part each drift by their own amount as the room warms. A dispute can hinge on where and when each side measured, a legitimate physical effect nobody may ask about until the argument has escalated.
Two operators, one room
None of this needs two organisations. Two instruments side by side, run by two people trained slightly differently, can disagree over the same part measured minutes apart. Formal studies exist to quantify this: several operators each measure the same batch of parts two or three times on the same instruments, and the spread is split mathematically into the share from real part-to-part difference and the share from who held the instrument. The people involved are often surprised by how much of their disagreement was never about the parts. A process never checked this way has no basis for claiming its numbers would agree with a second, independently run process.
Agreeing the method first
The way to avoid the argument is to agree the full measurement method in advance, in the drawing or the contract: the instrument class, the technique, the calibration traceability expected, and the reference temperature and conditions. Then both sides are provably measuring the same thing the same way before any number is compared. Once two parties are each insisting their reading is correct, the cheap resolution has gone, since the fix was always to agree on the tape measure before either side picked one up. A measurement is a number plus a method, and arguments end only once both halves are on the table together.