As JW said had he been drinking? Qualified on the 744? Licence and documentation with him? Familiar with company SOPs? Are you aware of the individuals training history?
Could he be a Walter Mitty?
Way too many variables to make it a no-brainer I'd think.
Personally, unless the situation was incredibly dire, I'd go with company rated, sober and current given the choice.
I'd agree it is not a no-brainer.
It will be via the CC you are made aware of their existence, so they will be the first assessment as to sober(ish) and character. I doubt I'd need to see their licence, and not interested if familiar with company SOPs - we're hardly following them single pilot as it is.
You will have to brief and discuss the role of the pax with them.
Google gives:
# - CHECK IF A TYPE QUALIFIED COMPANY PILOT IS ON BOARD TO REPLACE THE INCAPACITATED MEMBER.
and the presence of any type rated company pilots on board ascertained.
Interestingly our QRH gives more latitude, but I will not quote from here. Boeing 737 NG FCTM:
...consider using help from other pilots or crewmembers aboard the airplane