Dave,
I've not found this to be the case. When I kept tanks with mediocre lighting, i.e., 1 watt per gallon or less, algae was a constant problem, especially that long blue slightly coiled stuff that grows from the edges of plant leaves. But once I started using moderate lighting, 1.5-2 watts per gallon, and added floating Indian fern [or similar] I've never had algae problems of any kind whatsoever. I don't bother with CO2 and my tanks all have rich substrates based in part on pond soil. I barely ever use plant fertilisers. These may be factors.
My honest belief is that once you add enough lighting for fast-growing plants, you tip things against undesirable algae. At worst you get diatoms and green algae, but these are both trivially easy to fix with a few nerite snails. I cannot stress too strongly how well floating plants help here; they seem to be the silver bullet in my tanks at least. I know the Amano brigade aren't into floating plants, but if all you want is greenery that keeps your fish happy, floating plants are the best!
Cheers, Neale
if you want to make the situation in a tank with algae worse, just add more light.