Hello, Jasonb.
First, the example about UFO's was to show how in less than 30 years a fantastical claim, in this case the earth being regularly visited by beings from another planet, can take hold of the popular imagination and even believed by many, despite the lack of verifiable evidence, despite regular debunking by scientific experts, and despite the fact that there could not have possibly been eye-witnesses. But in fact, there
are eye witnesses -- people claim to have been abducted and brought aboard alien space ships. How is this any different from your claim that there were eye witnesses to Jesus? You are the one saying that there could not have been enough time before the first Gospels to be written for the Jesus legends to develop. I am merely pointint out that fantastical legends can develop in a very short amount of time.
So, seeing how quickly legends can develop, even to the point where we have "eye witnesses", how are the Jesus legends sufficiently different to preclude this? I recall that about 40 years is the accepted time between the alleged ministry of Jesus and the writing of the first narrative Gospel.
Remember that Jesus was not the only faith healer at the time -- in fact, we have actual historical records of real faith healers. In fact, we have faith healers today. Faith healers were a normal part of the cultural milieu in those days, so I don't think the authorities, even if they did want to debunk this Jesus cult, would have bothered too much to check out stories of this sort.
At any rate, when did the Jesus cult become so powerful that it needed to be thoroughly debunked? Probably long after the fact, after most of the alleged witnesses had died or been dispersed and impossible to find, and after enough time for many people to "remember" having seen Jesus in person. Before that time, it was probably considered sufficient to simply throw the heretics out of the synogogue when they showed up.