I think I can weigh in on this one, since I'm staring at a collection of Sagan's works resting on the shelves of my bookcase.
The movie made some changes to the source material, as all movie adaptations do, but the basics are still very much there. The author of the source material - Carl Sagan - was not just a scientist but a bit of a celebrity who used his popularity to provoke general audiences into different ways of thinking. He wasn't this rigid "hard science" guy and he wasn't above stretching the truth a bit to tell a compelling story.
And "Contact" is a story. A work of fiction. Sagan's first and only novel. So I'm willing to forgive him for stepping outside the boundaries of hard science. I'm also reasonably certain that Ellie is kind of a version of Sagan. A protagonist who is a scientist, but who also has a deep sense of wonder at the universe revealed by science. Her reactions to seeing those wonders up close is the sort of thing I'd expect out of a guy like Sagan. He was not a dispassionate observer. He was a passionate advocate for science.
Watch the first episode of "Cosmos" and you'll see...he invites you to take a journey in a "ship of the imagination" across the cosmos...complete with stirring music and Sagan staring off into the void...enraptured by the beauty of it all.
Ellie isn't some backwoods redneck who had a "UFO encounter" with some swamp gas. She's a scientist who had an encounter with a very real extraterrestrial intelligence. The twist is that there's not enough compelling evidence to convince anyone of what she knows. The destruction of and/or lack of evidence is, IMO, Sagan taking the perspective of the aliens. They've made contact with a race of apparently quite violent beings (the Hitler transmission as evidence) and have sent along instructions to build the machine. If the human race is as dangerous as it appears (and remember this was when we had lots of nuclear weapons hanging around, something Sagan felt very passionate about) then it makes sense to give them the opportunity to make one sojourn out into space to have a brief meeting, then make it very, very difficult to repeat the journey if the meeting goes bad.
Can humans make the machine work? Or perhaps more importantly, can the human race deal with the "Contact" itself? Ellie represents the human race pretty well, so they send her back, but hedge their bet by covering their tracks. Now it is up to humanity - if they can manage to avoid self destruction AND deal with the fact they're not alone in the universe - to start working on a way to get back into that system of wormholes and interact with the rest of the galaxy.