Yes seriously, here is what they asked me on first order with them:

"Since you're a new customer with Hetzner, we ask you for a scan of your passport or ID card (authenticity check). It's only necessary for your first order with us.

Please send the scan by fax or as an email attachment."

When they say they delete it after 21 days, as they did in the mail I've just received, I trust them. I find their communication on this matter, as well as previous matters, open and serious.