When a PGA Tour player shoots a really low round - 61, 63, 59… whatever… ask yourself: did the guy have to get up and down a lot or hole a lot of chips for birdie? Or did he hit a bunch of greens, leave himself short putts, and have a decent day with the putter?
When a PGA Tour player needs to rely on his short game, he probably didn't have a great round. He may have salvaged a decent round, but he didn't have a great round.
Great rounds - and good scoring over the long haul - are a result of the full swing. Hitting greens, and hitting it closer to the hole where you have stress-free pars, are key. The days when you make a bunch of putts or happen to stick it close? Those are your great rounds. The rest are just good rounds.
I'm not sure anyone has ever chipped in six times to shoot a net 65, but they've stuck a bunch of shots close to do it a ton of times.
Your short game is your crutch. It's there to keep a great round going, or it's there to bandage up a bad round and keep it being an "okay" round.
Your full swing is the main determinant of your score. The days you hit it well are the days you have good rounds. If you have a little luck or hole a few putts, they become great rounds.