This is just because they communicated poorly that they require proof of your ability to legally be employed in the USA. Passport and SS card both fulfill this requirement. I'm as WASPY stereotype as you can ask for, I've had the same check done at every job I have had in the past 20 years. For me it's easy, because I always have a passport card in my wallet anyways.
Anyone can have a Driver's License, however the newer DLs in many states have the optional citizenship validation and marking, so those can be used as well.
DL/State ID is proof of identity. You can have such documents and not be eligible to work in the US.
SS Card (unless stamped not for employment or the electronic equivalent) proof of eligible to work.
US passport proof of identity and of citizenship, and of course citizens can legally work.
Probably 99% of US Citizens will have some combination of these as their I-9 eligibility documents.
Permanent residents will likely have a DL/State ID and their green card.
If you look at the I-9 page https://www.uscis.gov/i-9-central/form-i-9-acceptable-docume... there are a significant number of other documents, which many HR departments seem completely unaware of, like special endorsements on foreign passports and special eligibility documents, or military IDs or Tribal IDs for proof of identity.
Anyone can have a Driver's License, however the newer DLs in many states have the optional citizenship validation and marking, so those can be used as well.