I have a memory of a short story in which a plucky group of scientists and researchers (and maybe students?) invent a machine that allows you to view any place and period in history. It will revolutionize historical studies, but almost immediately the evil G-men of the oppressive government are after them, trying to seize and destroy their machine, muzzle the scientists, etc. etc.
Finally one of the G-Men catches the scrappy group of heroes. And in a trope-breaking moment, we realize the evil government isn't really evil at all, but has realized what the scientists didn't - that being able to view any point of history anywhere on the planet will include "history" that happened just a second ago. All privacy will be lost forever.
The scientists realize the implications of their discovery and agree to get rid of the device, but one ashen-faced scientist (or student) reveals that he had just mailed the plans for the device in the mail to a journalist, so they would be distributed to the world even if the scientists were caught. The story ends with the G-man grimly welcoming the scientists to a new world of no privacy.
UPDATED: The story is "The Dead Past" (thank you, user14111!)
I can't think of any other stories that have explored this idea - the scrappy heroic underdogs fighting a faceless, repressive government... who turns out to have a very good reason for trying to suppress what the heroes are trying to do. Are there any other stories that have explored this interesting twist on a common trope?