Markham's response is typical of the weird denials the reporters will hear over the course of the film.
MARKHAM: I assure you there's nothing very mysterious involved.
Markham is based on real-life attorney Douglas Caddy, who was found in contempt of court when he refused to testify against his clients, even though attorney-client privilege grants him the right to do so. Caddy believes he was targeted because he was a closeted homosexual in a harshly homophobic environment. (Source)
LIBRARIAN: The truth is, I don't know any Mr. Hunt.
Remember Markham the lawyer saying "I'm not here?" This denial is just as plausible, because not five seconds prior the librarian was sure she had retrieved material for Mr. Hunt. The White House isn't even trying to make their denials appear valid. They think they'll get away with it.
BETTY MILLAND: There's often shredding. We do that a lot.
Shredding documents in 1970s is similar to Hillary Clinton having a personal e-mail as Secretary of State in 2015. Government documents aren't supposed to be shredded or deleted. There's supposed to be transparency.
BERNSTEIN: In other words, by their very silence, there was a cover-up.
You've heard that honest people have nothing to hide. If that's the case, then there is no reason people shouldn't talk to Woodward and Bernstein. By not conducting interviews, they're not risking being put into a position where they have to lie, which would be worse than not talking.
JOE: I followed my orders. Period.
This one little line makes the Nixon administration seem super-shady. All the government employees are just following orders, but where does it stop? Would they do anything they were asked, like kill someone? Or wear a polyester suit?