Yes, you are spot on. If you ever get a chance to go to Merlefest--Steep Canyon plays it about every year--you will see a bunch of kids who are already unbelievable musicians because they had guitars, banjos, or fiddles put in their hands as soon as they were old enough to hold them. Where I live (in Appalachia, and you better know how to pronounce it :)), there are scores of bluegrass family bands. Some make it big, while others go no further than playing summer barbecues, church socials, and county fairs, though they may be just as talented. It is most definitely part of the culture, just as you say. A lot of kids here grow up hearing it and playing it. Not all of them become Alison Krauss or Steep Canyon Rangers, but some do.
If you ever get a chance, check out my neighbors, Balsam Range. Their music is right there with the Steep Canyon Boys, and Buddy Melton is as good a tenor as you'll hear anywhere. Great recordings, too.