Humans VS machines in the 60s-70s:
one way of putting this accomplishment in perspective is by regarding the results of the match between Bobby Fischer and MIT Greenblatt computer program (Running Mac-Hack, a software written by the great Richard Greenblatt himself) in 1977.
I do believe that in 1977, Fisher was still very representative of what humans can do at their best at chess (even though he was retired), and so was the MIT Greenblatt computer for the machines. Still, Fischer obliterated the machine (3-0). This was 12 years after Hans Berliner won his title.
Now going back to your question, it seems fairly obvious that the gap between Greenblatt's computer and any computer 12 years older is very considerable. However, it appears to me that the gap between Fischer and Berliner is not that big. This is enough evidence for me, that, as a master, using/trusting a computer in 1965 was completely inappropriate, if not to say suicidal.
From the programmer's perspective:
Berliner entered Carnegie Mellon in 1969 (4 years after his title) to do his PHD, where he came with the idea of programming HiTech, a chess engine. From Wikipedia:
It performed well, but only until it ran into transitions, that is, points in the game when the balance between the players changed. This led Berliner to conclude that HiTech was weak in board evaluation.
He then gave up on solving chess and focused on another simpler problem: Backgammon. His first prototype was released in the early 70's. It took him nearly 10 years to achieve a strong level after he applied principles from fuzzy logic. Once again, Wikipedia:
in 1979, BKG 9.8 was strong enough to play against the ruling world
champion Luigi Villa. It won the match 7–1, becoming the first
computer program to defeat a world champion in any game [..] Berliner
states that the victory was largely a matter of luck, as the computer
received more favorable dice rolls.
He then goes back to trying to solve chess, and re-develops HiTech (with other big names of chess software, like Murray Campbell) and he finally obtains a computer program with master strength (2500~ elo) in 1985.
Temporality of events does not line up, according to his own words in the early 70's "HiTech was weak in board evaluation." It's only 20 years after his title, (which corresponds approximately to two eternities regarding advances in computer science) that he obtains a software having the strength of a master. Said software would have probably not won the world ICCF championship at the time, as it was still way weaker than the super GMs of the 80s.
If he used a computer in 1965, either the computer was garbage and would have been completely ineffective, in which case Berliner would have been stupid to use it, or he had a 2600+ strong software at the time, and then faked the next twenty years of his life by developing 1800+ software to hide his secret.