There is no difference between the mechanics of paying with credit card and paying with a debit card, at least in Norway and Sweden. I hold up my card to the reader and sometimes enter my PIN. I'm not even sure if there is a way for person accepting the payment to tell if it's a credit or debit card I'm using.
I've seen Americans try to pay with a credit card in a supermarket in the Netherlands and have it fail.
I've had places fail to accept my Swedish debit card in the Netherlands. It's more to do with some places only accepting local cards rather than debit vs credit cards.
Maestro and Visa Electron are already or soon will be full discontinued. How can you even tell a debit and a credit card a part nowadays? The only distinction between my credit and debit Visa cards is a single word sign in a tiny font at the back (I live in a EU country).
So unless those Americans are trying to with Amex/Discovery/smth similar cards I'd find this really surprising.
Even a decade or two ago Germany was the only country I've been to where it was only possible to pay with these regional debit cards in some places. I really don't think this was an "Europe" wide thing for a quite a while now.
I don't know what the hangup is (maybe it needs to be reported to the Dutch government since it's obviously coming from a NL national?).
Until then, we'll have to keep using a low limit credit card or Paypal for many online purchases.
People in Europe tend to only use a credit card for online purchases outside of their own country; most people don't have a credit card at all. Online purchases tend to be done with national systems like the Dutch IDeal (this even works with large international shops like Amazon and Steam).