I’m guessing the pro really knows his student’s game, which is why the pro gave that specific advice. PGA Scrambling stats as a whole last year show that the Tour average was a hair under 58% Cantlay led everyone with a little over 2/3. If this student has a much lower scramble percentage, like the 5-10 percent I vaguely recall reading is true for the average golfer, then yes, that’s a lot of strokes being left out there. Not to mention that scrambling is often not a matter of the difference between par and bogey, but if you really botch it, it can be the difference between par and “other.”
For most -3s though, I’m not thrilled with the logic behind it. As I see it, to be a 3 handicap, a player is already hitting a ton of greens in regulation. Likely over 50 percent. (Comparing again with the Tour GIR, average is a hair under 2/3 and Cameron Percy leads with nearly 73%) Unless they’re much worse than expected around the greens, and are constantly taking three or more to get down, this player’s issue likely isn’t chipping/pitching, for the 6-9 greens they miss.
It’s that most of their first putts are outside of their reasonable-make range. The solutions to that—especially if the guy is complaining about bad putting—is to either improve putting fundamentals (establishing the line and speed, address, stroke) such that the reasonable-make distance increases, or honing their approaches so that they can be closer to the hole.
Our host had a chart in his “Breaking 90” piece that showed putting distances and make percentages for Tour guys, scratch players, and 18 handicaps. The difference between Tour and 18HDCP for making 2/3 of their first putts, was going from 6 feet out to 4 feet out. Two feet. That’s it.