Am I being lied to?

Having worked in a bank I totally agree that the best thing is to take the card to the bank. Your mother should take proof that she lives at the address and if she has something like a letter about her council tax, showing the 25% deduction for living alone, that would be good.

Before opening a bank account she'd need proof of her address. Simply saying she lived there shouldn't have been enough without that proof.
If everything was above board gf could have asked for a note from your mother confirming her own address and that she was living there temporarily.
I'd contact the bank directly and point out that no permission was given to use the address.
Also ask why they accepted this as adequate and that the account should be cancelled.

Exactly what Jane says don’t deal with the girlfriend deal with the bank direct

My gut reaction is that your mother should advise the bank that the g/f doesn’t live at her address and she didn’t give permission for her address to be used.