From what I've read, it's because algae generally uses different light wavelengths for photosynthesis than coral zooxanthellae do - corals using more blue light, and algae using more red and green/yellow.
For a simple explanation, here's a graph from Khan Academy about photosynthesis and light absorption:
I wish I could find the graphs that I've seen specifically for corals/algae, but I can't remember where I've seen them. Anyway, basically the "Windex" blue light tanks use that spectrum (and some people recommend it over using white/red lights) because - at least theoretically - the corals do fine using primarily the Chlorophyll A provided by the deep blue while essentially starving out the algae by not providing the green/yellow and red lights for Chlorophyll B and Beta Carotene. I've seen some more complicated charts of this with more absorbing pigments than just these three (Chlorophyll C, Chlorophyll D, PSC, and PPC to name a few), but - again - I can't find the ones I've seen for corals which would be more useful, and this one gets the point across.
So, the theory is that you feed the corals with blue light, and the algae with other lights. By reducing the other lights, you stop feeding the algae/give the corals the competitive edge. That's why people say to reduce intensity of other colors to stop algae. How accurate that theory is would likely depend on the specific corals and algae involved, but the theory
seems relatively sound when speaking broadly. Since many (possibly most) algae species utilize Chlorophyll A, I have no idea if it's effective or not, but there is a chance that it gives corals the edge they need to beat out algae. I'm not aware of any studies that actually show one way or the other though.
With regards to the "... old ones grow algae!" - here's a quote from Dana Riddle on it that basically says it's possible following the same lines of reasoning listed above, but he's not (or at least wasn't) sure if it was true:
In case you're curious, here's a graph from the paper linked below that shows different classes of algae use different spectrums of light for their photosynthesis: