That video does make this sort of thing a bit ridiculous:
Two Scottish supporters of Hearts soccer club were sentenced on Monday to an eight-month jail term. The two Hearts supporters were arrested by Greek police after trying to enter the Toumba stadium in Thessaloniki with flares, where...
Certainly for the super league. No idea about lower leagues. I think you might be able to get round it with a passport and buying the membership (usually 10 euros) if you buy the ticket from the ground prior to the game (perhaps they can override the social security number requirement). However...
I think there is little chance of getting a ticket in the home end either*. Over here they require you to register for a fan membership and provide your greek ID and social security number to purchase a ticket.
*The caveat being that this is Greece so there is probably a way round it, but given...