Bing also caches AMP content: https://blogs.bing.com/Webmaster-Blog/September-2018/Introdu...
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.
I guess you're making a minor technical point, and it's technically correct. Someone else could do AMP better. But until someone does, why not shorten "Google's implementation of AMP" to simply "AMP"? Is there any other?