Yeah no. You can take the subway to a LIRR station called Jamaica or a parking lot in Howard Beach. Neither is actually at the airport let alone within a mile of an actual check in counter.
NJ transit isn’t a subway, and even so you still can’t take it to Newark Airport. You can get off a mile or two from the nearest terminal. Utterly inexplicably, the PATH train, which is reasonably described as a subway system, stops an entire stop short of even doing that, despite the tracks continuing onwards to that AirTrain station.
Once you get off each of these subways, in a location that is near to, but definitely not in, an airport, you may choose to take a slow and oddly expensive rubber wheeled bus that sort of is a monorail (and is certainly not a subway) device onwards to a terminal.
And of course at LaGuardia you can’t do even that.
So yes, it is “really true” that you can’t take the fucking subway to the airport.
All you have to is try it, get off the subway, and then ask “am I in an airport now?” and if the answer is no then you’ve figured out the problem.