First off, let's just shed the hotbutton word "evolution" and agree to limit ourselves to the use of "adaptation," shall we? We both agree upon the presence of adaptation, setting the attribution of wildly differing implications of that adaptation aside for the moment.
Now that we're dealing with a term agreeable to us both, let's just boil that previously assumption-loaded question down to a less freighted essence, and that would be:
"Why would bacteria that respond by adapting to stress survive better than bacteria that did not adapt to stress?"
The answer is rather evident, wouldn't you say? They adapted in order to survive. There's that purpose bugaboo again, one with which I have no issue, but one that makes your position untenable.
Then, there's the aftermath of such adaptation to stress and all the tortured meaning attributed to that. At this point, we part ways. You have no evidence of speciation due to environmental stress, any more than you have evidence of inbreeding leading to speciation.
Therefore, my position is actually the more logical of the two, since I'm relying upon facts in evidence, and you're speculating.
Then it is Darwin's theory of adaptation through natural selection of genetic variation; and this is an elegant example of it, and in this case variation is increased during stress by inducing mutation that allows for a greater rate of adaptation.
So if this adaptation is such a great mechanism to solve biological problems presented by the environment, what is going to prevent the DNA from diverging in separate populations until it accumulates to as much as say, between a mouse and a rat?