I have talked to people playing games with those rules, so yes, you're not the only one questioning this - but yeah the problem is there is no way to calculate Steadfast (hence it cannot exist) outside of combat.
And once you do calculate Steadfast, it's done in a certain way - a way that doesn't take anything else into account than the combat in question.
The Detachment Rule is superimposed on this, but says nothing of changing the way Steadfast works except that it is passed on to the Detachment should it occur (just like all the other Special Rules - and again, Steadfast is not a Special Rule in that sense, it's not even listed as one of them.. Stubborn is, so Stubborn is relatively simple even though it leads to some silly situations as well, as we have discussed..