AMP's HTML validator has a hard dependency on cdn.ampproject.org [0]. So the hosting requirements aren't fully isolated, and entirely under your control.
Even then it's quite a stretch to go from saying Google controls AMP to saying the validator has an online requirement. Also, as the other commenter said, Google, Bing, and Cloudflare are currently the certified CDNs to get the icon in search results.
>The pages are hosted on google.com
Anyone can roll their own AMP pages and host it on their domains. For example: https://amp.reddit.com/r/AskReddit/comments/6yj6iw/what_did_...
This includes getting your own amp lightning icon in search results when you host with certified CDNs.