That’s a common misconception that’s been passed around the Internet so long that it’s become common knowledge. There’s a great (now deleted, but archived) writeup showing that the Wachowskis always intended humans to be batteries. The actual source of the “processors” idea came from a Neil Gaiman short story written to promote the movie at its release
When people claim that leaks “get people killed,” they’re referring to when undercover agents are identified while they’re in the field. The only secrets exposed in these leaks are the computer hacking techniques used by the US to spy remotely through compromised devices.
You could maybe say that closing off those surveillance channels prevented the CIA from learning about some attack, but that’s really tenuous. It also assumes that the CIA isn’t constantly developing new zero-day exploits so that they can continue to spy on just about everyone on the planet.