Not all of the people whose correspondence they leak accept public money, or are part of governments.

They don't have much of a moral hill to stand on - unless they subscribe to the morality of "The ends justify the means." (Which most people do.)

If the ends don't justify the means, then what does?

Exactly - certain means are perhaps inherently not justifiable. Consequentialism vs. other competing philosophical stances.

https://en.wikipedia.org/wiki/Consequentialism

I see. So the interesting moral claim is not "the end justify the means" (which is too obvious) but rather "For every mean there exists at least one end that can justify it", which is controversial.

Maybe you shouldn't use means that need justifying in the first place?

But then why do anything at all?