That's a risk you take by bringing in a minister you can't trust. It's actually (behind the scenes) easier for a minister to send assassins than a normal Elector. Hostile ministers are a bad idea!
(I'm thinking about this one and I can definitely see making the network investigation still available on someone loyal - it's RELEVANT to your ministers after all - but a lot of the other actions are all written from a perspective that would not make sense if they were your minister, so even without considering balance questions it would create problems.)
Just for fun, has anyone unlocked gur fxvyy yriry gb trg nhgb-onpxtebhaq-erirny?