it is unheard of for a rocket company to have two independent teams simultaneously building the same complete vehicle design in two separate locations.
Very true, though that's less a rocket thing than the reality of manufacturing complex systems in very low volume. With most complex gizmos, its simply not financially practical to have two separate facilities, each with their own full set of capital equipment, each with their own set of trained operators, etc. Even most [American] rocket companies have just one team to service their east coast and west coast launch sites.
What's most interesting about this competition is that it suggests a) they don't actually know how they really want to build it, and b) Starship is going to be fairly light on capital equipment (tooling, GSE, etc.) for the final assembly.
The closest thing in the space industry is probably one web, where there's one production line in Toulouse and two lines in Florida. Though...near as I remember the two lines in Florida are going to build the volume (the Toulouse line was more of a development exercise that they're going to use to build different spacecraft based on the oneweb bus.
Expanding to Aerospace as a whole, B and A have final assembly lines around the world and, at least in a conversation I had with one of the guys leading the A320 plant in Alabama a few years ago, it does sound like a legitimate competition with the other equivalent lines around the world, where each is allowed to develop their own nuances to the overall production process.