To say that Nick Fury doesn't trust the Asgardian would be both redundant and an understatement. Nick Fury doesn't trust anyone. On the other hand, there's not many people Nick Fury has set up multiple isolated Research-and-Kill teams for.
When the so-called god makes as much as the shadow of a wrong move, and people so driven by what they think is "right" always make a wrong move sooner or later, Fury is going to hit him with so much firepower that S.H.I.E.L.D. accountants are going to spend years hiding the bill in the national debt.
But not before then, of course. The Asgardian is useful, and has useful friends, and as much as Nick Fury doesn't trust anyone, he has no problems using people he doesn't trust until he no longer has an use for them. The Asgardian will live until he tries to betray them because of love, or his family issues, or whatever the fuck is driving Loki's insane smile this week.