First I will go by Airbnb's "Policy" for hosting first responders/frontline workers, then I will throw in my two cents....
"To host COVID-19 responders on Airbnb, your space needs to be an entire place without any other guests present." To me, this would indicate that the space is to be used solely by the first responder, and not other guest. The whole idea of self isolating, is so that individual does not cross contaminate anyone, especially considering people can be asymptomatic for 14+ days.
"Healthcare staff and first responders must be either affiliated with partner organizations or reviewed by Airbnb prior to check-in. This process helps ensure responders have a COVID-19 work assignment and are familiar with safety protocols. If Airbnb is unable to confirm a guest's COVID-related work prior to check-in, the reservation will be canceled." To me this would indicate that they are handling the tasks of verifying the credentials of first responders. How valid that verification is, I can not say.
Personally, I would decline those that attempt to bring others, including family. Are the scamming you? Maybe. The only way you can verify them, as you said so yourself, is asking for credentials. I am in a hospital daily that is fighting Covid 19. I can detest to the fact that 90% of us working there, are trying to avoid others, especially our families, at all cost. I would love to see my parents right now, but I would not want to risk exposing them. Personally, it surprises me that they are asking to bring additional people.
I think it is great that you, and everyone else participating in this program are opening their homes to others during this time. Unfortunately, there is always going to be those who abuse the system, and then there is the flawed system itself.
If possible, try changing your settings on your listing to make it so only one individual can stay. You can also update the verbiage in your listing to reflect that one person rule as well
Stay safe.