My old running coach, who was a lifelong golfer but not a low scorer, used to equate golf scores with your half marathon time, and it made a lot of sense. World record for half marathon is around 59:00, and the best any pro has shot in a tournament is 59. A lot of ok runners can run 90:00, and 90 for 18 holes is bogey golf which is sort of the standard for "ok".
Personally-2:54 marathon, 3 handicap for a few years. And that was a legit handicap with a fair amount of stroke play tournaments. As for cheating in golf, or bending the rules, that definitely happens but I saw it more with 10-20+ handicappers. When you get down to single digits the last thing you want is a lower handicap because you end up getting less strokes and paying all your buddies every weekend.
Jtupper-good question about how much work it would take to get to certain levels as a runner or as a golfer. For me it was about 4 years from when I started run training (had a decent aerobic background before that and ran some but no formal run training) to a 2:58 marathon and another 6 months after that to my pr. I was only a 50-55 mile a week guy and didn't do a whole lot of running during the winter most of those years. With golf it took me about 5 years to go from a 20 handicapper to a 6, and then another 2 years to get down to a 3. Going from 20 to 12 just took a lot of playing (4-5 days a week after work/weekends). Going from 12 to 6 to 3 meant playing 7 days a week (April-Nov since this is snow country) PLUS spending 5-10 hours a week practicing.
Personally, I think it would be easier to take Joe Couch Potato and turn him into a decent golfer than turn him into a decent runner, and I think you could do it a lot faster too. By "decent" (for a couch potato) I'd say sub 20 5k, or sub 90 on a golf course. I say that because running fast is more dependent on genetics where golf is more learning how to do it and getting it done-training effort being the same for the person trying to learn both sports. Plus, as tupper points out, you can spend a lot more time working on your golf game than running before fatigue sets in. I know a lot of people that no matter how much effort they put in they are never going to run sub 3:00 but I guarantee I could have them breaking 100 in a year.