It would depend on the course rating and slope of the tees you play on the courses you play. I can imagine someone who shoots well on a 6100 yard course who drives it ~ 210 who therefore maintains a respectable handicap, who would necessarily shoot an extra ten to twelve strokes just because almost every par 4 functions as a par 5 on a longer course.
Lame example, but there's a municipal course in Los Angeles called Westchester. It's 4339 yards, par 64, rating of 60.5 and slope of 89. It's ridiculously easy. It's so easy that shooting a -2 62 results in a differential of 1.9
(2 strokes over "scratch"). The golfer you describe could easily score well at that course and rack up low rounds, maintaining a handicap of like 2-6 or something with no problem, then transition to a course where every single par 4 is unreachable and shoot "blow up" rounds every single time.
Theoretically, the course rating and slope system should mitigate these differences, but in practice it really doesn't. That golfer would be shooting 85s and higher all day at a longer course, which would translate to something like a 12-15 handicap.
To your point, I do not see how that player could maintain a single digit handicap on normal length courses. I do see how that player could "game" the handicap system and produce a low handicap that could not travel.
EDIT: Also, the handicap system calculates your potential by selecting your best rounds - not your overall average - and then assuming that your potential is marginally better
than even the selection of your best rounds.
The formula to determine your differential score for a particular round is:
((Actual Score - Course Rating) * 113) / Course Slope
Then round to the nearest tenth
The formula to determine your handicap
depends upon how many official rounds you have recorded, but assuming you have 20 it is:
Take the average of your lowest ten differentials, and then multiply that number by .96
Instead of rounding, just delete all digits after the tenths.
That multiplication of the average of your ten lowest differentials by .96 is where the system assumes that a golfer is actually a little better than the average of their lowest differentials.
Also remember that you're just tossing out the worst differentials.
EDIT 2: Obv this is only the USGA system, I don't know what other countries do.