There is a lot of back story but the short of it is that neither Urgent Care nor a local lab would do it for me without a Dr referral.

I have read any pertinent information on medicare.gov and found no mention of any such stipulation or precondition.

I have called Medicare twice asking for clarity and was given no support. I asked both times for documentation that a referral was needed and pointed out that their website made no mention. I finally got this: "it requires a medical professional to refer you for the test, it can be a doctor, a pharmacist, or a drive through facility (which I thought was for the swab test only). I was also told that the offices have information that is not included on the website, to which I argued that left patients uninformed on the very topic it was intended to inform.