I wonder if they can handle chip and signature cards - which I believe you're entitled to ask for. I'm seriously thinking of changing all my cards back to one that puts the burden of proof back on the bank, rather than me having to prove why their systems may be insecure.
IIRC chip & sig cards can be requested - particularly if you're disabled (they're not allowed to ask you why) - and anyone that refuses to take such a card may fall foul of disability discrimination laws.