The problem is, these shows aren't meant to be intelligent. Life doesn't have much drama, so if a show was REAL then nobody would watch. A non-bowyer isn't going to be too happy when his Friday night tv dinner is ruined because a 40 minute show is 100% filled with a bloke making a bow over a period of 2 months. It's not tv.
Now, one could argue "don't show the fake stuff then" but lets face it... How many prime time shows out there even mention Osage bows, sinew backing, snake skin etc? If that adapted scene got one new person into making bows, or discovering falconry, then it's hard to say it's a bad thing.
We're all the same - everybody has passions about something, and if that subject appears on tv it's never shown properly because the rest of the public who don't give a hoot won't be interested in the details and will switch over. It's a nightmare being a professional musician because I can't watch shows like the voice or x factor etc as I know how insane the format is, but I love how many younger kids are learning to sing or play an instrument based off the shows. The moment they actually try it, the shows begin to look fake to them, they move away from the screen and learn properly.
Somebody watching mountain men might think bow making looks awesome, primitive, creative and so on, grab some wood, make some mistakes, research, learn, make more mistakes and so on until 10 years later people are asking him for advice on a Perry reflex because they saw a commercial for beer that was set in a forest where guys were shooting cans with hand made bows or something.... I dunno.
Point is, be glad TV went to the trouble to feature a hand made bow, instead of a shop bought recurve, and don't worry about details. Entertainment TV isn't there for learning, it's an introduction.