Connecting a higher-current power supply to a lithium-ion charger will damage the battery. Why?
Read your link more carefully. Fast chargers can cause damage; connecting a larger power supply to a correct charger will not. As you say, the charger limits the current. That's what it's for.

Terminology is confused by the public calling USB power supplies "fast chargers".

Edit in response to comment: The following uses "USB power supply" to refer to the thing that plugs into the wall and "charge controller" to refer to the charge monitoring system inside the iPad. This is not the same as the terminology in common use, but it's more correct.

Suppose that the battery's 1C current is 2A. The device is then designed with a charge controller that allows up to 2A into the battery. It is shipped with a USB power supply capable of delivering 2A. It charges quickly at 2A, limited by the controller, and everyone's happy.

Note that the USB voltage will be 5V but the battery terminal voltage will be &lt;4.2V.

Someone then connects a different USB power supply. These are normally limited internally to 500ma. The device charges at 0.25C more slowly.

I get impatient and connect it to my bench power supply capable of supplying 10A. The charger is now not limited by the power supply, but by the internal charge controller. It draws 2A and charges at the "fast" speed.

Older mobile phones and other devices put the charge controller and the power supply in the same brick that plugs into the wall, and do not do their own current limiting.