Many people would probably propagate a false idea if it got them fame and fortune but how many would actually perpetuate a false idea if it got us beaten, tortured, thrown in jail and killed, especially if it got us nothing in return?
We have records in and out of the bible that all of the apostles except John died excruciating deaths. Peter was even crucified upside down. Why would they die for what they know is a lie? Lots of people even today die for what they think is true but the apostles were all eyewitnesses to the resurrected Jesus so they were in a position to know its true. They were beaten thrown in jail and murdered for what they had witnessed and proclaimed. If the story was false and they knew it they would be stupid to be jailed, tortured and killed for what they knew was a lie, yet history shows us that not one of them recanted. It's interesting that the 12 men associated with watergate could maintain their story for weeks let alone years.
These excruciating details are evidence that shows these men encountered the risen Jesus and were willing to do what it took to spread the truth.