The bold statement would actually be up to the club. When you pay for golf, you pay for a green fee and a cart, so technically, they do have a right. Do I have a right to be there if I am just using the putting green?
I do it as well. I hate it when I'm at the golf course, see a water hazard, and say "I bet there's a 10 lber sitting under that log," lol. I've yet to ask a course if i can fish their ponds though, dont know why though.
I understand that it's not near the gentlemen's game it used to be, but look at the pros. They all wear polos and dress slacks practically. If I see someone sporting the tattoo golf wear, then my first thought is a hacker. Tattoos are a different story, but the tattoo golf is just stupid.