These are Teslas -- very high-tech cars. They have odor detectors that can sense the insulation in your house wiring starting to smolder
when it is drawing too much power and back off.
Seriously, though, as an EE I have a theory as to how they do this: the amount of current that a wire can (safely) carry depends on
the resistance of the wire (which, in turn, depends on the thickness of the wire); the more current you draw through a given resistance,
the more the voltage will drop; I suspect the car simply senses how much the line voltage drops as the current draw increases, does a
little simple math, and figures out what the effective current capacity of the line is. Of course, if you have a low-amperage breaker in
there it can't know that, so it will probably trip it. The car also knows the upper limit of each type of connector, so it will never try to go
over the maximum rated limit for any given connector type.
(Somewhat) related: has anyone ever had the car refuse to charge from, say, a 117v outlet? This happened to me recently when
travelling. I figured there were two possibilities: the 3-prong outlet wasn't actually grounded (alarmingly common), and the car detected
a ground fault just as a GFI would; or the rather ancient house wiring it was powered through couldn't supply even the minimum
current to do any reasonable charging at all.
I believe you are correct that the car also now has programming to reduce the current draw in response to voltage drops (pretty sure that was added in a firmware update a year or so ago.)
If you got a red light on the EVSE when it refused to charge, that would be the bad ground case. If the light stayed green, maybe it was the voltage drop? I haven't read of it refusing to charge entirely in that sort of case, but it seems plausible.
