After some searching around on the forums here, I found out that I'm not the only one with such problems.
I pay for all online game purchases and DLC with paypal. Works perfect with everything thus far, from EA to Steam to Ubisoft. With all of them I chose Paypal as a payment option, put in my name and password and I get the stuff.
Now Games for Windows/Xbox Live is the very first place that requires me to add a bank account or credit card. I don't own a credit card and I don't want to add my bank account and continue with direct transactions. When I learned something from the PS3 debacle then that giving your credit card information is never ever a good idea. That Microsoft requires this crap is ridiculous. It's not like I'm not used to being screwed by Games for Windows live, but this is final straw!
Maybe I miss something, but I don't see a way around this. And yes, my Paypal account has a goddamn positiv balance.
I think about just buying the games I already own on Steam just so I can buy the DLC hassle-free and will avoid GFWL in the future.