I assume there is a kind of permit system, given the "unless you have written permission from the government" part

You can apply for a permit - you usually only will get one for a specific area if you are an archaeologist associated with a university or a museum or something apparently.

The law is intended specifically to prevent random people digging up stuff and causing damage to historic sites.

‘When metal detectors are outlawed, only outlaws will have metal detectors’?

Man, I've missed classic Slashdot-style "didn't read TFA".