That is right, the key resides on stating that you are non resident that wants to open a non-resident account. But if you tell your story...something like I live in Spain I don't have the residence card but I want to open an account the answer will be no way.

In fact one of the fiscal reports Bank of Spain likes most from the banks is the PNR balance listing (Non resident account balances)

Nevertheless,remember that the case of a US national and a EU national are totally different, the later should have no problem at all in opening a nonresident account.