Very probable? How often do asteroid impacts happen on this world?
Judging by the dialogue from our heroes ("Meadows and not meteor craters?!") and our guest stars ("Our skies have darkened three times since the harvest"), apparently every few months...
That is, they would
happen every few months if not for the deflector. And the operator dying before educating his successor doesn't immediately mean that the next three asteroids would all crash through; apparently, the Medicine Man only needs to maintain
the device, and lack of maintenance eventually
allows an asteroid to hit the planet.
These are the consequences of hiding the truth about the Enterprise's involvement. Do you really think that letting them know the truth will screw them up more than misleading them in this way?
Oh, absolutely. Misguided theories come and go; contact with space aliens remains regardless of whether one believes in it or not.
Say, what if something like upper atmosphere ozone depletion here on Earth really were the doing of some alien species, and we completely misunderstood it? Our countermeasures have helped fight and perhaps even defeat the depletion, but the impact of this on human affairs in general has been virtually zero. Really, the extinction of the cuddly Tasmanian Devil is probably way more significant in terms of "promoting eco-thinking" or whatnot. If, however, the truth about alien intervention were revealed, Earth would be forever changed in ways nothing but the very extinction of our
species could rival.