They 'said' they had evidence. Lois saw none of it.
When Clark asked her if she believed their story, she said she believed they were blackmailing the government - she'd witnessed that herself.
Franklin Hodge came to Smallville to talk to them, and Lois witness him shoot them with an advanced weapon? Now he has taken them away, perhaps never to be seen again?
They were attempting to blackmail the government. Hodge's job was to deal with the blackmail attempt.
He tried to shoot her with the same weapon, because she had overheard his conversation with them? Later he tried to kill her by having a truck run over her? He demands that she give him a film that shores up the Sedgewells' story, and in return he will give her 'evidence' that Clark Kent is not an alien?
The film didn't shore up the story. The film proved they had met with Hodge and that he had had them removed.
The film implicated Hodge. That was why he had to destroy it.
He didn't care if Lois printed the blackmail story, or even if she printed the alien story. He told her 'Go ahead, print your story. It can't hurt me or anyone I protect.'
But the photos could hurt him - so they had to be stopped.
Really, if the Sedgewells' story was just another sensationalist UFO story, like the ones which claim that an Elvis statue has been found on Mars or that a woman in Minnesota had her alien lover's baby, why bother going to such extreme lengths to kill the story?
He didn't try to kill their story - he dealt with their attempt to blackmail the government (by having them removed). Only after he knew Lois had photos involving him, did he become desperate. He's the 'Invisible Aide.'
I tried to write Hodge as actually having a conscience - of sorts. He was perturbed when Lois said he was evil. He tried to explain to her - he just did what was needed to be done.
His first two attempts to destroy the film hadn't worked, (thanks to some 'Super' intervention). He already had plans in place to ensure the photos were never published. When Lois offered him a non-violent way to get the film, he took it.
If Lois doesn't understand that the Sedgewells' story must be true, or that it at least touches on some extremely sensitve secret, then she is so extremely stupid that the owners of the Daily Planet should sue Perry White for hiring her!!! 
Ann She saw no evidence the story was true - no space ship, no strand of hair, nothing. In her mind, the sensitive secret was that a couple of scientists thought they could wrangle a million dollars with an unsubstantiated story.
Maybe that makes her extremely stupid, but reporting the claims of 2 possibly deranged scientists as truth, despite a complete lack of evidence, is much more Nunk's style.
Again, thanks for taking the time to reply.
