"let the plant get as old as possible before allowing it to mature so that potency will be as high as possible during harvest"
Well yes and no. The statement is almost correct, but not in the way you've written it. If you were to say "let the plant reach sexual maturity before going 12/12 the potency will be as high as possible during harvest" that would be correct.
What does "let the plant get as old as possible before allowing it to mature" mean exactly? Maturation of a plant is when it reaches sexual maturity, this can happen anywhere from about 4-8 weeks for most plants in vegetative growth with most around 6-8 weeks. The other statement 'the older a plant is, the more cannabinoids it will produce, and therefore the more potent the THC will be" is also true. A 6 month old plant will produce more Cannabinoids than a 3 month old one. So the older a plant is, the more potent its buds will be.
When vegging plants, sexual maturity and age are two factors than need to be balanced off against time to harvest and size of plant. Because of this balance, most people tend to switch flowering when the plant reaches about 12 inches tall, regardless of how old the plant is.
This is one of the areas where clones have a distinct advantage over plants from seed, because all clones take the age of the mother, so an 8 week old plant produces 8 week old clones - these clones are therefore already sexually mature enough to flower and therefore the one area the grower has to decide is, how long do I veg for the clones for in terms of height and yield, rather than length of time for sexual maturity.