Measuring the OD of a thread is an almost meaningless exercise. Threads engage on the flanks not the peaks so you need to measure what's called the pitch diameter. A process that uses either a special micrometer that touches the flanks without touching the crests or roots. Pitch diameter can also be measured using wire of a known diameter and a chart to translate the results.

Note that threads are rarely 100%, and the crests are often truncated by varying amounts, but this doesn't affect the fit, something which depends on the pitch diameter, which few bike mechanics have any idea of how to measure.

As a practical matter, a decent mechanic can check your BB shell's threads by way of a crude gauge, ie a known to fit well BB cup, which he can thread in and check for radial play. Likewise your Miche rings can be checked the same way in another new frame. Radial play in BB threads used to be rare, but has become more common over the last few decades, especially among what I'd call B-class makers. But even among A class produces like Campy and Shimano Dura Ace, there's also variation with Campy generally having a tighter fit. Given the quality level, I suspect that it isn't an issue of sloppiness, but where within the standard tolerance they set their targets.

Even perfect threads can sometimes seem sloppy, and my preferred way to build them up for a tighter, no creak fit is to paint one or the other with nylon paint. This makes a tight fit controlled by the thickness of the nylon, while still allowing dis-assembly later