Jake, could a Android version upgrade be worth trying? If so, what's the latest version that F-Secure supports?
But not to 4.3 "Jelly Bean" as it has caused much problem so far, although it's looking better know:
Our latest build (8.3.13921) which was released today to Play Store supports Android versions up to 4.4.
Unfortunately Samsung S3 only has Android 4.1.2 update available at least in Finland though in some other areas 4.3 may be available.
In the BBC article it says 4.3 will begin rolling out to selected users in the UK, so it might take some time to reach all I guess.
But if there is an update for Brillo I mean, do you think it's worth try upgrading Android in this case? I think this is a very unique problem so it might not entirely be related to the F-Secure product. Just a thought.