Are there laws about the "Made in" claim? That is, could they realistically have the movement and case and everything made abroad, then only do the final assembly in the US and earn the "Made in the USA" brand?
Yes. In 2016 the FTC stopped Shinola from claiming their watches were "made" in America. Much more accurately they were "assembled" in America (Detroit) from foreign parts [1].
I entirely agree with the FTC, their claims were dishonest. As a point of comparison, Switzerland regulates what percentage of the watch must be Swiss before it can be claimed to be "Swiss," but it's not an easy question. For example, with completely made up numbers, low wage Chinese manufacturer sells mostly finished movement for $20 that required 4 hours to make. High wage Swiss assembler puts in another hour, at a cost of $40. Total time is 5 hours, 80/20 Chinese/Swiss and total cost is 60, 33/67 Chinese/Swiss. From time perspective, it's a Chinese watch, but from cost perspective it's Swiss.
They already are. Their web site claims that they're using a Swiss movement. They're silent on where the case and other parts are being manufactured, but I'd guess that the movement accounts for a good portion of the production cost.
