I thought this was overblown at first glance but reading into it...
From Wikipedia:
Accountability software typically functions by continuously making screenshots of the user's mobile phone or computer screen and monitoring their internet traffic. It checks both for keywords (such as "gay" or "porn") and images associated with the behavior the software is intended to detect.
So like even if the Speaker is on a VPN securely viewing classified material, if it's on his phone or laptop, Covenant Eyes now has screenshots of it. That is very much a breech of national security if that is happening.