I don't believe there is anything close to the level of interrogation (necessarily augmented by attempts to corroborate claims by locating documents or interviewing witnesses) that you describe above could actually be going on.

They're not necessarily going to corroborate your claims by locating documents, but they absolutely review the documents you have with you. They'll ask you for your passport or other documentation showing your identity, and they run you (and your fingerprints) through every relevant database they have:

Once an asylum seeker is referred for a credible fear
interview, USCIS asylum officers conduct a
mandatory check of both TECS and the Department
of Homeland Security (DHS) IDENT database.
IDENT (the Automated Biometric Identification
System) is managed by the Office of Biometric
Identity Management (OBIM), which is part of the
National Protection and Programs Directorate of
DHS.

The person’s 10 fingerprints are electronically
submitted to the IDENT database, where they are
stored and matched to existing fingerprint records.
This is used to confirm identity, determine previous
interactions with government officials, and detect
imposters.9 OBIM also checks each person’s
biometric information against a watch-list of known
terrorists, criminals, and immigration violators, and
verifies the information against its entire database of
fingerprints to determine if the person has used an
alias or is using fraudulent identification.
USCIS asylum officers also ensure that FBI name
check and fingerprint checks have been initiated.10

The FBI electronically searches fingerprints within
the Integrated Automated Fingerprint Identification
System—the largest criminal fingerprint database in
the world—which includes some 73,000 known and
suspected terrorists processed by the U.S. and
international law enforcement agencies.11

Meanwhile, you're detained while all of this is going on. And all of the results of these checks are taken into account in making release assessments. The credible fear interview doesn't involve days of cross-examination or document review - but it's far, far longer than the few seconds of interaction you have at a customs desk, and it doesn't happen until DHS has spent several days of background checks on you.

If you have no identification, and no other way to corroborate your identity, you're going to be incredibly likely to be detained indefinitely. It's just literally the dumbest way to try to enter the U.S. if you're a terrorist - starting off in detention, having every background check known to the U.S. government being done on you, and then having to have a one-on-one interview with an immigration officer who is specifically trying to catch people who are making up their credible fear claims out of whole cloth (which you are doing).

humanrightsfirst.org - Credible Fear Feb