Not true. Intensity is defined as momentary effort. If you pick a weight light enough to do 20 reps and despite your best effort you cannot do 21 reps that 20th rep is going to be your most intense reps. I assume you never tried the 20 rep squat protocol that was so popular many years back. You don't need heavy weights, or even any weight at all, to maximize intensity of effort. A sprinter going for a world record is pushing himself to the max and you can see how exhausted a sprinter is after less than 10 seconds of effort.
Where did you find that definition of intensity?
Wouldn’t we all agree that to increase intensity you would need to either do:
(1) More work in same amount of time
(2) Same amount of work in less time
Work = force x distance
So it’s easy to see how to do more work:
(1) Heavier force moved the same distance
(2) Same force moved over a longer distance
In this instance force is the “weight” you’re lifting and distance is the number of “reps” you’re doing.
If you think about it, it’s no more difficult than that.