I worked with someone years ago who was from Scotland. We became friends and he invited a few of us friendly co-workers to a party to meet his family, who were here on vacation. Now, I had never had a problem understanding this guy, but around his family, his accent became so heavy that, try as hard as I could, I did not understand more than an occasional word here and there. But, I also ran into that once with someone from the deep South (US). I'm usually quite good at adjusting my ears, but somtimes, it just can't be done. We all speak differently and I think that it is simply a matter of practicality to adjust to whatever the dominate language or accent is in a given situation. I did not expect his family to change their way of speaking, but neither did he expect all of us at work to change to his way. As far as someone saying you sounded like a relative from the "old" country, maybe they were just trying to find a way to relate to you.
P.S. Living in a town with heavy Scottish influence, I have heard bagpipes played both horribly and beautifully. The one thing that did not work for me was a Christmas parade a few years back, where the local bagpipe brigade was playing Jingle Bells. Just did not go together!
P.S.S. I am heavily Scottish descent, so no prejudice implied here at all!