The 2 scenarios you outline are in no way symmetrical/ analogous.
In the first scenario, you are the boss. If you say that the flight is off, disappointment apart, there is no pressure on you not to exercise your judgement.
In the second case, the punters didn't pay you to cry off at the last minute. They're paying you good money, maybe in cash, for you to get them there and they don't take kindly to last minute hitches.
Actually they are. There is a direct comparison because in both cases there is a risk of “gethereitis” causing a bad decision, it’s just driven by different motivating factors.
In the one case a desire not to deprive a 95 year old veteran of what may be his last reunion with old comrades with whom he risked his life 70+ years ago, in the other pressure from a type alpha passenger whose attitude is: “I’ve paid and want to fly”. (FWIW, in my case the former would probably be the harder to resist, but I’d resist anyway!
)
My ability or inability to make the right decision is the same in either case and depends only on my ADM skills, willingness to use those skills to make an objective decision and the determination to implement it.
Note: this is NOT a comparison between a pilot with a CPL and all its associated training vs a PPL/IR, it is the latter either being paid or not for the same flight and, again, I stress: this is in no way in support of grey charters which are illegal and should be stamped on.
And, by the way, even an ATPL doesn’t necessarily immunise a pilot against this kind of bad decision:
https://en.wikipedia.org/wiki/Smolensk_air_disaster