I can explain how it works...the local pond company makes money by selling you stuff. Very, very common issue.
Luckily you understand more about ponds then most people. You are absolutely correct about the UV doing nothing for you because of the pond type you have. I'll add UV isn't needed (probably) because you say your water is clear...but green. That makes me think the green is just the light interaction with string algae, and/or other macro type algae. I've heard this before, can be confusing. So that we understand "clear" would mean you can see stuff underwater. Then there are levels of clear. Seeing fish or you hand 1' below the surface, seeing fish 4' down, seeing shadows of fish on the bottom, etc... "Clear" generally means very little suspended micro algae and therefore UV can't improve that.
UV doesn't kill string algae.
You have clear water and string algae. Hear that a lot. I hear about people with green ponds and no string algae, clearing the pond water and then dealing with string algae. I'm of the opinion, with some testing, that string algae produces a chemical that kills green water algae. Norm Meck (2006) found water from clear ponds killed green water algae almost on contact. An experiment that is easy to reproduce. His theory is the chemical is produced by a bacteria. My theory is it's produced by string algae. It's a very common trait in the plant world and has been seen in ocean algae. And I did some experiments adding string algae to green water which convinced me enough.
To me string algae is something to control rather than try to eliminate. Here in AZ grass carp (White Amur) are used to control sting algae and they do an excellent job. Impressive fish to boot. Most states ban or control their use. Here a special permit is needed and only sterile fish can be used. Don't know where you live. But there are other fish that eat string algae.
There are also oxidizers that can be poured on to the string algae to kill it, or the entire pond treated. Very temporary and for your size pond and that it isn't lined I wouldn't bother with chemicals at all. You also then have a bunch of dead algae to deal with. There are tools (rakes and such) for pulling string algae out. Normally only done when it's a serious problem, so maybe once a year.
Trying to eliminate a specific nutrient or sunlight to control string algae is normally a losing battle. In a non-lined pond there is absolutely no way it can work. I wouldn't worry about nutrients, they are what they are. It takes very few nutrients for algae to grow, even fewer to stay alive.
