I cannot find a foreign passport in any list so of accepted documents so that's why I would accept them rejecting it.
They do have options for people with out DL/ST-ID (it gets pretty interesting in the secondary list. Yearbook pic???)
https://travel.state.gov/content/travel/en/passports/how-apply/identification.html
A problem people run into when they apply at the post office (or other third party) is that the person behind the counter flat out refuses to accept documents that are on the DOS list of approved documents. So yes the USPS can ask a lot of things, but they are not there for that. They are only there to accept the application take the fee and forward it to the DOS. If anything is wrong or unclear it's the DOS job to ask for further info.
Personally I'm getting annoyed by desk staff who not only are wrong in their assumption but need to be pleaded with (not polity asked) to look at their own manuals of what is and is not allowed. DMV staff not knowing to accept certain NOA's, SSO not knowing to accept I-551 stamps, Banks, USPS, HR etc, etc. And If I have the time and energy for it I will take on that fight every single time.