Yes, several car rental companies run a credit report for debit card users. I had a client last month totally freaked out by this since his credit was less than stellar due to difficulties a few years back, even to the point he had a backup car res made at a higher cost with another company.
I was told by the corp. headquaters of the car rental company that the person checking you in doesn't see your credit report, just that you are good to rent or are declined. It's all based on closely guarded credit criteria that they had no access to to tell me about, and can vary in different parts of the country. They did tell me that if the problem is in the past and the current report is OK my client should be fine.
That said, the client told me he had absolutely no problem with the orginal car rental company, though they did tell him (and me ahead of time) that there would be a hold of a few hundred dollars over the estimated total rental amount that might tie up his card.