Ultimately, someone needs to have the keys, and they do, which is why they go through additional screening. Since there's a whole team, they would either have to collude or cover their tracks very well. Considering a major part of their job is keeping our data and our users' data safe, a breach like that would not be taken lightly.
So ultimately, it may be possible for one to snoop on our users, but it's much easier to trust (and keep tabs on) a small, well screened team than the entire company.
Speaking personally, I can say that I would (and do) absolutely trust my own data to our sys admins.
What additional screening do you put your system administrators through? Are we talking security clearances and background checks? Definitely curious to hear the specifics.
Can you ask? I'm curious to learn what these background checks entail. Also, if they actually do prevent bad apple's from joining, why not do them to programmers as well (given that they have the power to program backdoors etc into systems).
I'd introduce some more checks and balances if you can. Even Google got burned by a rogue engineer snooping on people, a lengthy interview isn't enough.
It doesn't really matter if you put someone through extensive interviews and then hire them, or if you use a third party who can't afford to lose its reputation, it all comes back to trust, which is why David's post is so on-point.
So ultimately, it may be possible for one to snoop on our users, but it's much easier to trust (and keep tabs on) a small, well screened team than the entire company.
Speaking personally, I can say that I would (and do) absolutely trust my own data to our sys admins.