It sounds that way to me too.
How do you define stress? I ask because I think there's a misunderstanding afloat.
There *are* differences between environmental change which just causes increased mortality and/or decreased fecundity (reproductive success) in a species, and environmental change which actually "stresses" an organism (i.e. which causes significant enough biochemical changes in its cells to result in a boost in mutation rates). For a trivial example, consider higher background radiation, or mutagenic chemicals in the environment, but higher mutation rates can also be induced by more mundane environmental conditions, like being hotter or colder than the organism can tolerate well, or required nutrients becoming no longer available, etc.
But as previously mentioned, this doesn't cause a different *kind* of evolution to occur, it just generates more mutational grist for the mill of natural selection.
It's interesting that not only do more mutations occur when they might be most "needed" (i.e. when the species has a need to adapt more rapidly), but also some genomes seem to have mechanisms which *actively* turn on a higher rate of mutation when certain environmental conditions are met, and not just as a passive response to a breakdown in normal error-correction mechanisms. Such things would be expected to arise through evolution, whereby an organism "evolves to better evolve".
For example, here's a paper on the topic of what is called "adaptive mutation": Stress responses and genetic variation in bacteria. Also: Adaptive amplification and point mutation are independent mechanisms: evidence for various stress-inducible mutation mechanisms
and, that's why I say evolution is not random, because the "survival" mechanism of a life form provides bias.
Hans Selye, endocrinologist and author of the General Adaptation Syndrome," defined stressor by the physiologic response. That was back in the 40's. Today it has been shown that stressors can be vague, diffuse (e.g., chronic anxiety) and yet be deleterious (and yet a selective pressure). Mice in a colony will kill certain others, mostly low ranking contenders for alpha status. If you watch the process carefully, you'll see the mice mob the victim and harass by posturing and hisses. The victim eventually succumbs by dying...but with not a mark of violence. Later they'll eat his carcass...the stressor? (vagal death). I could go on absurdum with examples which illustrate the essence of evolution is not found in the stressor but within the response.
So, yes, ...higher mutation rates can also be induced by more mundane environmental conditions...