Not remotely true. The iPhone is designed to gracefully accept charging from, for instance, Apple's iPad chargers, which provide either 2x or 2.4x the power of the bundled iPhone charger. There is no evidence that this degrades the battery.
Now, if you use crappy 50-cent third-party chargers, I don't know what happens.
You say it’s not the but it is my exact experience of them. Happens every time. Tried it a few times to be sure it’s that. Using a Belkin dock and an Anker charger. Both decent enough brands.
It's up to the phone how many amps to draw from the charger. Just because the charger has a higher amp rating doesn't mean that the phone is drawing more current from it.
Voltage is applied, current is drawn. It’s basic physics. You’ll fry a phone by connecting a charger that operates at a higher voltage level, but it’s perfectly harmless use a charger with a higher amperage rating
Now, if you use crappy 50-cent third-party chargers, I don't know what happens.