Visible crew/equipment: As Ellie runs up the stairs of the observatory after hearing the first audio transmission from space, she runs towards doors with two large glass windows in them. As she opens the doors, a crewman/cameraman is visible in the right window for a brief fraction of a second.
Visible crew/equipment: During the scene when Ellie has discovered the Signal, and is in the control room with the guys, she turns to one of them and says "Make me a liar". Right when she turns, you can see some bright, smaller, roundish white lights reflected in her eyeglass lens. These are probably camera lights, as their appearance wouldn't match the computer screens or natural lighting in the room.
Chosen answer: Ellie defended her version of the facts with everything she had to work with, but the simple fact was that the government cover-up was just too strong for her to overcome. The points you raise are perfectly reasonable, but the version of events released by the powers-that-be denies everything that happened and, without any other proof, Ellie has only her word to convince people with. For some, that's enough, as we see in the film, even if a majority choose to believe the "official" version.
Tailkinker ★