Nah. Unless it differs by state, which I guess it might. Here are the questions:
1. In the last 14 days, have you experienced any of these symptoms? Select all that apply
You can answer whatever is accurate, including "None of the above"
2. In the last 14 days, have you had contact with someone who has a suspected or confirmed case of COVID-19? Count any contact that lasted longer than 15 minutes, closer than 6 feet away.
You can answer either yes or no, as appropriate.
3. Are you seeking a COVID-19 test because you have either recently returned from travel or are planning on traveling soon?
This one is answered Yes, and that qualifies you for a free test. (Edit: Actually, I just made a test appointment and got approved for a free test even answering no to everything. So maybe it's free no matter what you answer.)
Then there are questions about pre-existing conditions, pregnancy, vaccination status, and whether you've ever had Covid.
Maybe it differs by state, if the testing is state funded. But, aside from the free Walgreens Rapid NAAT travel tests I've gotten in New York state, I've gotten a free Walgreens Rapid NAAT test for travel in Florida too. And Florida is about the most Covid-skeptic state there is.