Even if it is paper filled, it has a digital it will be electronically recorded of which, if you create an account and add your case numbers, you'll have access to receipts and history of your case.
You don't need the watermark paper, though you're required to have it all times. CBP / DMV can just input the case or scan the barcode at the bottom. So, the print from online account should be sufficient. Watermark just adds authenticity, should anything be called to question.
I never carried mine anywhere.