Yes, of course pyrethrin will harm beneficial insects, and aquatic organisms as well. More importantly, the system most assuredly contains piperonyl butoxide as a synergist (there usually is way more PBO than pyrethrin in the mixtures). I don't believe the effect that PBO has on the livers of any mammals in the area is a good thing. Another goofy thing about the mosquito mister companies is that they have a variety of recipes and appear willing to change the formula. One of the first changes I would expect is to see them add permethrin, which is a fairly bad thing to be misting in the open environment and can be deadly to cats. One of the problems is that most homeowners don't know what the effects of the various ingredients are or even what the ingredients are. If they did, they probably wouldn't use them at all. Bluntly put, the commercial mister systems should not be used.
Now, the typical fine print in the mosquito mister companies' promo is that the system repels the mosquitoes. So, why don't they use garlic tea in the misters, which is a proven repellent? I think the answer is two fold. First, they don't think they could sell it (maybe it has an aroma, maybe it's hard to convince the public that it works, the companies that make the systems haven't tried to adapt it to garlic, or maybe the people that run the companies are too ignorant to consider garlic). Second, and unfortunately, some dopes patented garlic as a mosquito repellent. How they overcame the vast body of prior art and usage is beyond me, but maybe nobody mentioned it. Anyway, the prospect of a patent may scare off the commercial applicators, but it alone should not deter home users. As to the mechanics of using garlic in an automatic mister, that might be a different story and a research job. I would say that anyone who insists on using a mister repellent setup should use garlic; I'd bet that is as or more effective than the toxic formulas in that usage.
As for the reference to pyrethrin being synthetic derivatives, I believe Mr. Clean meant "pyrethroids." As usually used, the term "pyrethrin" is the naturally derived substance. By the way, permethrin is a (synthetic) pyrethroid.
In theory, theory and practice are the same; in practice, they aren't -- lament of the synthetic lifestyle.