that's not 100% true tiptop.
Algae, like plants, needs sufficient light to grow. Most people who have the 'came with the tank' light don't have algae problems (aside from the typical brown 'algae' diatoms, which aren't really algae, or blue-green algae, which is actually a bacteria).
So a low light planted tank really doesn't have any more algae than a non-planted low-light tank.
Algae, by the way, is always caused by a nutrient imbalance, when there is sufficient light present.
You are, however, correct in that higher light tanks without
CO2 injection having nasty algae issues. Under high light,
CO2 is used up too quickly, and the plants cannot utilize the nitrate and phosphate present, thereby opening the door for algae to take hold. At 1.5wpg,
CO2 starts to benefit the plants, and defintely stunts algae growth. At 3wpg,
CO2 injection is pretty much mandatory, unless you like the look of algae and sickly plants.
(
BTW, its' the carbon in
CO2 that plants need...they split the
CO2 molecule during photosynthesis, which is why plants give off
O2, and is how carbon supplements like Flourish Excel work)