When Moses didn't come down from Sinai, the Jews requested a replacement leader, explaining (Exodus 32:1) that
this Moses man who lifted us out of the land of Egypt — we don't know what has become of him.
Rashi, as often, considers "this" to refer to something present and visible:
The satan showed them something like the form of Moses, that they were carrying him in the air of the spread-out sky.
Of course, Moses wasn't actually dead.
Fast-forward some forty years to Aaron's death. He died and was left on a mountain, while the Jews were nearby, not on the mountain. Numbers 20:29:
The entire people saw that Aaron had died.
Rashi wonders how they saw what happened atop a mountain:
When they saw Moses and Eleazar descending — but Aaron did not descend — they asked, "Where is Aaron?" and he told them, "He is dead". They told him, "Is it possible that the angel of death can have dominion over the one who stood before the angel and stopped the plague?". Immediately, Moses begged for mercy and the service angels showed him, placed in a bed, to them. They saw and believed.
Why did they believe? That sort of evidence had been proven untrustworthy.
Source: This question (worded differently) was included, with no answer offered, in the weekly Torah Bits publication by the St. Louis Kollel, volume 20, issue 40, June 28 (Chukas), 2014.