What is too big of current that will fry the voltage regulator?

dhenry:
The answer will depend. High voltage (even with very small current) can kill it. Lots of current (even with very low voltage) can kill it. Middle current + middle voltage (lots of power dissipation) can kill it too.

So the datasheet features of a typical (here a 7805)mean nothing and are simply lies?

The internal
current-limiting and thermal-shutdown features of these regulators essentially make them immune to overload.

Lefty