What does it mean to say that "the 1/2-inch chuck/collet/whatever is really machined to 12.7mm"? 0.5 inches is exactly 12.7 mm, so what else would it be machined to?
Yes 0.5 inches would be exactly 12.7 mm but that comes from the way the inch is now defined (which is 1 in equal to 25.4 mm) as opposed to the earlier definition (i.e. 1/12th of a foot (this definition being the older imperial definition).
machined to 12.7 mm simply means that the original imperial definition is abandoned for imperial units and although the chuck/collet/etc is still sold as 0.5 inch chuck/collet/etc; when constructing it, it was measured in the SI units of mm for precision purposes.