That fire is used as an excuse for every deadbeat falsely claiming military service. It was a big deal but the VA has a comprehensive program to recover lost records. If direct evidence is lacking they will investigate based on many other sources...Such as the below:
Statements from service medical personnel.
Certified buddy statements or affidavits.
Accident and police reports.
Employment-related examination reports.
Letters written during service.
Photographs taken during service.
Pharmacy prescription records.
Insurance-related examination reports.
Medical evidence from civilian/private hospitals, clinics, and physicians that treated you during service or shortly after separation.
We will accept photocopies of any service treatment records that you may have in your possession.
As to ID, he may not have proof but he does have fingerprints which can be verified. As to the extent of VA records lost see this link:
https://www.benefits.va.gov/COMPENSATION/NPRC1973Fire.asp
I'm not believing that in 18 years on the street he never applied for help from the VA who would definitely have investigated.