This is incorrect per the Immigration and Nationality Act (INA).
Foreign nationals that are lawful permanent residents of the U.S. must present a Permanent Resident Card (“Green Card”, INS Form I-551), a Reentry Permit (if gone for more than 1 year), or a Returning Resident Visa (if gone for 2 years or more) to reenter the United States. U.S. LPRs are not required by the U.S. to have a passport for travel, although most foreign destinations will require you to have one to enter their country. (LPRs that are out of the U.S. for more than 180 days are subject to new immigrant inspection procedures as per 8 USC 1101.)

The difficulty can be the lack of knowledge among airline personnel who may not allow you to board without what they consider they proper documents.(Usually a passport and visa, if needed). Airlines are very strick about enforcing what they consider is needed, as they can be hit with substantial fines for allowing pax without the required travel documents to board.

A US CBP officer may ask for a passport as they will have the same question Fly-Me-to-the-Moon! raises, namely, how did the person enter the other country without one. But as others have pointed out, it is possible for citizens of some countries to enter their own country without a passport. An LPR without a passport can obtain a Re-entry permit and visas for other countries can be put in that. Both the I-551 and the Re-entry permit are lieu travel documents recognized by the US that can be used in place of a passport.