It's perfectly legal (and common) for a decade now to scan documents and destroy the paper original as long as you follow some guidelines. Keyword is "ersetzendes Scannen".
And yes, they care about those rules and that you provide "originals" according to that definition - in particular that you didn't modify digital documents in any way. You can (and should) comply with that and there are service providers to help if you are to small to set that up yourself.
Thanks, today I learned about "ersetzendes Scannen". I just checked and it's exactly a decade (2013) since it's allowed which coincidetally is the year when I started working as a freelancer (and I have to care about such rules).
I admit that my last paragraph was kind of hyperbole, but I never heard (at least from other freelancers) of a tax inspector which wasn't happy with either everything printed or everything digital. I guess they really start to care if they suspect something fishy.
And yes, they care about those rules and that you provide "originals" according to that definition - in particular that you didn't modify digital documents in any way. You can (and should) comply with that and there are service providers to help if you are to small to set that up yourself.