. . . While the single hit will stay for 2 years, it should not affect my credit in a bad way, it is just the fact they did it without my tacit approval that bugs me. I want to warn my employees and send them to other companies if needed due to this policy . . .
Your Dollar experience is informative for any traveler and especially those who use debit cards. But I do not see corporate malfeasance on Dollar's part or the fault of a secretary or travel booker as some suggest. I myself have never thoroughly read the Dollar fine print, but as I can now see, it is indeed instructive that we all maybe take the time to read our contracts thoroughly if not at the counter, then at the hotel or in the airport lounge when we have time on our hands. As to tacit approval . . . the world is bigger than any of us as we expect immediate results/gratification for ourselves but extend impatience/indignance when others do the same to us ( not that I do not agree with privacy/consent limitations which IMO are moot in this instance ).
A single credit check does not dink one's overall credit standing -- banks and agencies who regularly run credit checks understand the process and they can divine the context of an entry when evaluating one's credit worthiness. We've all got unsolicited checks on our records as a bank seeks folks to solicit for credit cards or a used car dealer tries to figure out if you can afford that shiny car you're casually shopping around for.
The OP makes a good point in that it is easy to grab the wrong card when they look alike, and this could be important as debit cards and credit cards do indeed work differently. I do not carry my bank's debit card ( I get my cash from my wife

) but I think I'll remind our son to be wise and judicious if he uses his.
Barry