The new feature is that Google's browser displays your domain, obscuring the fact that Google is doing the serving. The change is what is displayed, not the server.
What Google actually means here is "We make AMP pages _appear_ to come from your own domain".
That's something entirely different.
This whole thing is just more doublespeak.
When I had a website with embed videos from other sites, I had user contacting me because the other sites had some problems. They couldn't tell the difference between megavideo/youtube/dailymotion content and my site, so they came to me and blamed me.
So what this means is that not only Google bullies you into putting your traffic under their control, but now, any problem on their part will be blamed on you by the user.
I hadn't even considered that. Add to this Google's notoriously absent customer support department and you have a recipe for a lot of frustration.
So Google’s browser now directly lie to the user about what’s being loaded?
I bet the SSL mark is still there though?
How can anyone trust this Googlan horse?
This is why you don’t make a browser and control major web-assets at the same time. These lines should not be muddied.