Iphones and our phones (and others) can gauge the amperage they are receiving and let you know that the low amp charger (slow) is delivering less than the higher amp chargers (fast). If a device not designed for a higher amperage charger is plugged in, it could overheat, so the generic chargers usually are lower amperage so they will work with a wide variety of devices, albeit at slower charge rates.
Your explanation is a good overview, but there are a few parts that I disagree on.
I've never had any problems with devices overheating due to being plugged in to "fast" chargers with 2 amp ports. Sure, the battery might get a little warmer because it's being charged at a faster rate, but it doesn't cause any issue unless the battery is defective. (Otherwise, how could those 6-socket 10-amp chargers exist without blowing up every device they connect to?)
I don't think the phones measure how much amperage they're receiving. Rather, the resistors in the USB chargers act like a key to a lock. The phone says something like, "Hey, do I see 1000 ohms between pins 2 and 3? Yeah? I must be hooked up to an authorized charger." Then they will adjust themselves to draw more amperage.
I just did an experiment to try and figure this out further. Out of three chargers, I could not get the phone to complain about any one of them. And I had one that could only put out 550 milliamps.
This charger is capable of 2.4 amps. It is the most powerful of the three, you can see the phone is drawing about 790 milliamps and there is no voltage drop.
imgur: the simple image sharer
This charger is the 550 milliamp one. You can see a severe voltage drop and a draw of only 510 milliamps:
imgur: the simple image sharer
This is the charger that came with the phone. Again, 790 mills but there is a pronounced voltage drop of 4.9 volts.
imgur: the simple image sharer
I would have expected the 550 milliamp adapter to cause the phone to throw an error, but it didn't. I'm thinking that the circuitry in the meter fools the phone into thinking it's plugged into an authorized charger.