Americans commonly use "tyre" and "wheel" interchangeably. Drives me nuts especially in motorsports where the distinction is important. But it is what it is. This was a case of a wheel coming off.
Not sure if I missed your joke. But this is probably a joke based on the spelling of the word being British. So Americans use tires and the British use tyres.
I wasn't joking, I'm not going to use the American spelling just because I'm talking about how Americans use the word. They really do use "wheel" and "tyre" interchangeably.
I'm an American, and I disagree, mostly. I've never heard someone say a "flat wheel"; it's always flat tire. Also if an American says a wheel came off when they mean a tire, they misspoke/misunderstand what they are talking about. There are plenty of Americans that know next to nothing about their vehicle despite it usually being the most expensive or second most expensive thing they own.
Disclaimer: Midwest USA here, can't speak for other parts of the US.
You're right, they do. And I'm certainly no expert, but I have a more difficult time imagining a tire coming off the wheel intact without some catastrophic "blowout" impeding it's ability to smoothly roll than I do imagining a whole wheel coming off.
Leak, low pressure becomes no pressure, various lateral forces encouraging the tire to fold this way and that under mass, and soon enough the tire alone escapes its tormentor (because it’s being bent and pushed in ways similar to those that originally encouraged it to pop onto the wheel) and scurries away toward an unsuspecting fence.