Basically it's a way for google to promote web pages that are better formatted for mobile devices that use a limited subset of html and restrict use of javascript. The pages are hosted on google.com as additional assurance that they will load quickly.
I do believe it's scary to some because it seems like it's giving google a lot of power and control over content on the web.
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.