The reason both for people being skeptical and for the landing to have maybe been faked seems obvious to me-too much money had been spent on the space program and too much more money could be spent on it later for the moon landing goal to not be achieved.
Then you have absolutely no idea how difficult it was to engineer and design hardware capable of putting two people, not only ON the moon but in designing a single stage to orbit vehicle to get them back and rendevous with a craft with enough power to get them back.
And every landing but one, was successful.
to put in perspective: at the time of Apollo's announcement, the US had managed to put on man in space, not in orbit, for a few minutes past the Karman line on a modified Redstone missile. They had to go from there to conducting these flights in less than a decade. Nothing like that had ever been done before, or since. It was the peacetime equivalent of the Manhattan project. Funny now nobody denies that nukes are real.
to make Apollo work, they had to learn how to develop:
large first stage engines (there has never been an engine as large as the F1 since)
develop cryogenic engines (the J2's are still studied to this day)
build the infrastructure for building, assembling, and moving skyscraper sized launch vehices
build the tracking network for tracking deep space objects
design and use integrated circuits
develop the first true computer user interfaces (the DSKY interface for the AGC)
learn how to live in space
life support design and testing
orbital rendezvous
orbital docking
orbital mechanics
landing a vehicle vertically on an alien world using only manually operated thruster rockets
training
capsule recovery
lunar sciences
safety enhancements (many redesigns after the fatal Apollo 1 fire)
launch abort system design and testing
lunar activity suit design and manufacture
precursor probe missions
and that's just a small list.
if they'd spread it out over decades it might have cost less, but the impetus may have been lost and perhaps no one would have ever went. The Soviets finally called it quits after losing too many N1 launch vehicles.
Yes it cost a lot. All of that, done in a hurry, and it was, cost billions, and would cost far more now. Look how much Gateway (LOP-G) is going to cost. Look how much ISS cost. Space is expensive.
It's like not believing Carnival has a fleet of cruise ships worth billions because dayum you can take a weekender on one for $300!