Does everything that is “Made In” somewhere have to be built completely from components also made in that country?.
No, but at least a good proportion of the finished product needs to actually originate from where it claims to, plus the design should also come from the claimed country of origin.
I regard shipping in far-east manufactured bikes in bits and doing a bit of final assembly then claiming them to be British/Italian/Whatever to be a downright dishonest practice. If I was to buy an "Italian" bike, I would expect the frame more than anything, to have been completely fabricated from scratch in Italy. Not in Vietnam, Taiwan, China etc.
I have several old Raleighs and a rigid Dawes MTB in my bike stable - and every single one of them has a British-built frame, mostly hand-built lugged & brazed Reynolds tubes, so the raw material was also made here. When I ride one of these I can honestly say it's a British bike, it isn't an import with a British maker's badge stuck on it, who are trading on their previous reputation for making decent bikes. I'm not saying the far-east stuff is all junk, it isn't, but if you are selling bikes with say a Vietnamese frame, you should be honest about it, and not try to pass it off as a home-grown product when it isn't. Some buyers may not care, but I do, and that's one reason I run old stuff and don't buy new badge-engineered bikes.