If it were true that long-term low level radiation were unquestionably harmful, you'd expect to find a clear negative trend.
No, that's not what we'd expect to find at all.
We'd expect to find at the high end a certain level of radiation that is absolutely lethal, and as the dose is reduced, the impact would drop down steadily, until a zone where life expectancy is reduced. However, that life expectancy is more or less on an absolute scale, and must be compared to the life expectancy of the species being exposed. An insect may survive high doses of radiation simply because it wouldn't normally live long enough to exhibit symptoms, while a longer-lived animal like a human will likely survive long enough to get cancer that ultimately causes death.
At a very low dose, the chances of having any noticeable symptom from radiation is unlikely enough that it could equally likely be caused by millions of other factors, so usually nobody cares. There is still a negative trend in survivability, but it's dwarfed by all of the other fatal conditions.
Too little radiation and the species dies due to inability to keep pace with changing environmental conditions.
Radiation isn't the only mechanism for mutation, though. Rather, it's the fast and cheap way to make a lot of mutations really fast, usually in places that cannot possibly contribute to evolution.
In order to change the species, an offspring's DNA must be mutated. That's dependent on a few thousand cells out of the trillions in a human body. Those particular cells are the ones involved in meiosis, splitting and reassembling the DNA that will become half of the offspring. During that reassembly process is where most mutations happen, usually by random chemical processes rather than any radiation. This enzyme doesn't successfully react with that protein, so a gene gets skipped or altered or inserted... It is extremely rare that a gene is altered by radiation during the process.
Once an offspring's development begins, though, the effects of mutations become more pronounced. If radiation mutates a single cell during early stages of growth, that fetus will develop with a cluster of mutated cells. Unless those cells are destined to become a gonad, however, the mutation will die with that generation, and the species will not change.
Similarly, radiation affecting a mature individual is is unlikely to have any positive effect, as the mutation is almost always either destructive or irrelevant. The proper functioning of a human body requires millions of interactions between tens of thousands of proteins, so randomly changing one protein is more likely to break something than to add new functionality. Of course, as before, even breaking something is only going to affect the species if it happens to occur in a cell involved in reproduction.
It is important to remember that evolution is never towards anything. It is away from an inability to reproduce (usually due to death). As an illustration, you must realize that you are the result of an unbroken line of millions of ancestors dating back millions of years, and every single one of those millions of ancestors were fertile and successful in mating. There is no scorecard in evolution. Either you pass on your genes, or you don't. It doesn't matter if your changing environment caused you severe illness or discomfort. As long as you manage to find a mate and make a child, you've won the natural selection game.
In short, radiation is a purely random occurrence with purely random effects, and the odds of any particular radiation-caused mutation being beneficial are so absurdly small that it is absolutely safe to say that overall, there is no safe dose.