I agree that there is a UX problem to solve (the address bar should show the original URL, copying it should preserve the original URL, etc) but whether the webpage got loaded from the original site or from some AMP cache is irrelevant.
It looks like Bing has the same problem, and serves AMP from bing-amp.com.
I agree that there is a UX problem to solve (the address bar should show the original URL, copying it should preserve the original URL, etc) but whether the webpage got loaded from the original site or from some AMP cache is irrelevant.