AMP pages are served from the publisher's server as usual, but Google can easily direct their users to their cache instead of the official site. Every AMP page also includes JavaScript hosted by Google, so Google gets pinged every time someone visits an AMP page, even if it wasn't through their cache.
"Google products, including Google Search, serve valid AMP documents and their resources from the cache to provide a fast user experience across the mobile web."
So it's Google who does deliver from the cache. Moreover, they motivate others to do the same on the same page.
Yes, Google can direct its own users to the cache, and others can also link to the cache. But if you or someone else link directly to the page, it is not served from Google's cache. Google would not be able to track those visits except for the fact that the page also loads content (at the very least, the AMP JavaScript) from Google's servers. AFAIK, it is not considered "valid" if you serve the JavaScript yourself.
I'm just a casual observer and that's just how I understood the idea.