So in effect, you would be using the past, which does not exist, to confirm something else from the past. And if you repeat the process a thousand times, with a thousand different pieces of evidence, together they would still be nothing but impressions of the past supporting other impressions of the past. (page 39-40)
It sounds like a weak argument. By that reasoning nothing is certain (except maybe that statement). The premise seems to be that since the past doesn't exist therefore anything that happened in the past doesn't exist, or that is not really able to be know. Therefor none of us know for certain that we were born, as that happened in the past (even if someone told us about it who was there, like your mother, wouldn't be certain as she is only relying on memories to tell you). We don't know if we paid the last bill, as that happened in the past, and if we were to check our bank statement, as soon as we put that down, that event would then be in the past so we will not know for certain again if we did pay the bills. This throws out the historical method, all forms of learning and also common sense.
The reasoning the old man gives is because our brains shuffle the information we receive into what we what it to be:
ordinary people will alter their memories of the past to make them fit their perceptions. It is the way all normal brains function under ordinary circumstances. (page 40)
This seems to suggest that reality is a shared hallucination (pdf). I am certain that the brain can be tricked but also that things (that happened in the past) can be known for certain.