UV sterilizers are good for decimating populations, but by their very design they cannot kill 100% of any pest in the tank.
Consider an example of algae. There are two rates that are important: the growth rate of the algae and the death rate. The population of algae will change, either the population will increase or decrease, until the growth rate is exactly equal to the death rate. Now, what the two rates are equal to depends on the environment: the food available, the lighting, and of course, the population of algae that is there. I.e. the food available to each cell of algae changes depending upon how many algae 'mouths' (cells) there are to feed. So, when all that equilibrates, the death rate is equal to the growth rate, the population remains constant.
Now, introduce the UV. What this does is increase the death rate. Well, the population will be reduced, but eventually, the population will get to the point where the death rate is equal to the growth rate again. There will always be some remnant population. It may be 99% of the original, 99.9%, 25%, whatever. And you may be happy with that.
The problem comes up when instead of dealing with algae, you use the UV to fight a disease, like ich, for example. Because there is always a remnant population, using the UV alone you cannot completely rid your tank of the disease. I think this is where the origin of the 'UV sterilizers weaken your fish's immune response' myth comes from. Because there is a small population of disease left over, it takes some time, maybe weeks to even months, until the population grows back, and your fish show symptoms of disease again.
Another way to look at this, the UV sterilizer can only treat a very small percentage of the tank at any one time. There will always be some algae or ich or bacteria that will not swim through the UV chamber. This is because the output of the UV is returned to the tank, and that re-mixing always occurs. And again, in the case of disease, if you ever take the UV out, the population will start to grow back.
Compare that with a medication you mix into your tank's water. The medication treats the entire tank at once. No matter where the ich or bacteria swims to, it will be attacked by the medication.
So, my conclusion is that a UV light can help to decimate, to quickly lower the population of a problem in your tank. But, if you are treating a disease, you have to then take the UV out and finish off the remnant of that population with a good, effective medication. Otherwise, the disease will takes its time to grow back and will rear its ugly head again some time in the future. So, like many things, UV is not a magic bullet, but it can be very effective if you know its limitations.