Foreign born people do not have to answer these questions. Only those born here, who did not have their birth recorded within a year of it, and/or who were not born in a medical facility would be required to answer the impossible to answer questions. Therefore only they would not be able to get a passport. The foreign born would not have a problem getting the passport. I guess the president is safe.
Seems like a hoax to me. How could this information be verified even if someone did remember it? The questions are for people not born in the USA. Even in the USA, it would be next to impossible to verify records for natal care given by doctors who are retired or dead and who kept their practice's records on paper which is probably destroyed. How much harder would it be to verify these records in a foreign country?