This is totally true. One of my regular courses is quite easy and wide open (Woodley Lakes). But the back tees are pretty long, which makes the differentials there much better than they feel like they should be given how easy the course is:
Blue: 6,805 yards, 71.9/119
White: 6,528 yards, 70.5/117
There's no way I shoot 1.5 strokes worse from the blue tees. On average I must gain at least a 1 point in average differential from playing the blues versus the whites there.
Though there are some courses where this would not be true. As someone who's pretty long, if playing a shorter set of tees turns a bunch of 400-420 par 4s into 360-380 par 4s, then suddenly I can tee off with a 3i or even 4i instead of 3w/driver and still be hitting a scoring iron into the green. Then the percentage of the time I end up in a penal spot off the tee drops significantly and I will probably score much better. Just turns out that at this course that doesn't really happen, just makes the shorter par 4s even shorter and the longer par 4s slightly less long, but doesn't really push any of them over that threshold for me, and only helps a ton on one par 3, turning a 6i-8i, depending on tee placement, into a wedge.
Yeah, it's definitely not always true. Totally agree that if a shorter set of tees is going to allow me to hit an iron instead of a wood oftentimes, then I'm probably going to score better because I'm going to be able to hit more fairways. Same with the par 3's as well. (This course was only 1 club difference on the par 3's so it probably wouldn't have changed much)
One example: A slight dogleg right par 4 that was 374 yards long with sand traps at the dogleg such that I needed to lay up with a hybrid. If I was playing a shorter set of tees, all I'm doing is laying up with 4 iron instead of hybrid, or being stupid and trying to hit a big cut with a driver beyond the bunkers. It's going to (basically) be a wash if I play it safe, and over time, likely going to actually RAISE my score from the shorter tees just from being stupid.