The page is still yours. You have absolute control over the branding, the analytics, the monetisation. Just because it happens not to be served from your domain doesn't mean it's not yours.
Let's also not forget that AMP is actively encouraging alternative caches: Cloudflare Ampersand[1] was announced literally an hour after my post. It's a whitelabelled AMP cache aimed at solving this exact problem.
Let's also not forget that AMP is actively encouraging alternative caches: Cloudflare Ampersand[1] was announced literally an hour after my post. It's a whitelabelled AMP cache aimed at solving this exact problem.
[1]: https://www.cloudflare.com/website-optimization/ampersand/