>That's the bit that sounds odd. Surely they can't just claim you're not a suspect yet and therefore deny you a lawyer?
IIUC, In a non-custodial situation, they are not required to provide the Miranda Warning[0]. However, the rights mentioned in that warning exist and are in force regardless of your status (custodial/non-custodial). One may invoke them at any time. I recommend doing so loudly if you're within two or three meters of law enforcement.