Chargers and Brands?

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http://androidforums.com – I have read that a generic charger can damage a cellphone. Is this possible damage only a matter of build quality of the charger, or is it a phone <-> charger compatibility issue? So basically I'm asking do I need a motorola charger to charge a motorola phone safely, or could I use an HTC charger for example, as long as it fits? On a related note: I recently had a smartphone that came with a generic charger, whenever the charger was plugged in the touchscreen had issue with being over-sensetive, like if I pressed "1" on the dial pad, it might hit 3 other buttons not even near (General)