I had a similar experience at Marks and Spencer the other day, of all places. The cashier was falling over herself with adoration for my supposed Irish accent. And this was based on a simple "Hello!" and "Thanks" from me. *shrug*
My dad does have a proper west of Ireland (Mayo) country (khun-three) accent that has been very Americanized after 30 years in the States...and even he doesn't sound a thing like me, the born and raised Midwest US girl.
They don't sound anything alike. At all.