The distinction that I'm making is that it's not that Vanguard being an anti-cheat gives it the ability to read things from your computer, it's that all regular programs on your PC can access basically everything.
Every game you install, every program (Discord, Steam, OBS, GeForce Experience, Origin, Epic Game Store, Battle.net, etc etc) could read your browsing history and record your keystrokes.
Most programs are well behaved but it's not because they are restricted in their permissions (like phone apps) but because the developers have no interest in your browsing history (same with Vanguard).