So using fidelis intepretation, greatswords would ONLY pass along stubborn to their detachment IF they LOST a combat.
Does that make sense?
No, because Stubborn is a persistent special rule. A unit always has Stubborn though it only gets to use it to take a break test. Therefore, it can pass Stubborn to it's detachment.
Steadfast is not a persistent special rule.
Page 76 in the BRB directly contradicts this.
Stubborn units are always steadfast.
Tada! Persistent effect.
Steadfast is a persistent rule. Stubborn simply says you have it even if you don't outnumber the enemy in ranks.
IF your interpretation was correct, and steadfast ONLY happened when you lost, then stubborn would also only kick in when you lost - as it simply says 'this unit is steadfast even if it has fewer ranks than its opponent'
Stubborn will not make a unit steadfast when it hasn't lost combat, using your interpretation.
Therefore you would still have to lose for the stubborn boosted steadfast to occur: and couldn't pass it on to a detachment if you hadn't lost a combat.
So, using your interpretation, greatswords are not stubborn unless they have lost a combat, and thus cannot pass along stubborn to a detachment unless they have lost a combat. Which is obviously nonsense.
You guys are getting confused with what steadfast DOES with how it is GRANTED.
BRB is quite clear that it is granted by having more ranks than the enemy.
BRB is also quite clear that what it is, is it allows you to roll break tests without applying the combat modifiers.
Honestly, arguing against the plain text of the rules would get you mocked and derided and you'd find yourself without opponents in my game store

I hope that Cruddace intended for the Detachment rule to work differently and they FAQ it to improve it, but as it is now, the wording doesn't allow it.
When you come up with an interpretation that literally does nothing, it's probably best to step back and re-evaluate your interpretation.
Maybe he meant that the detachment could use it's parent's ranks instead of its own to determine if it was Steadfast
Maybe, but that's not at all what it says right now. There's no support for the parent passing along its rank bonus to its detachment.
It's so utterly simple.
You gain steadfast by having more ranks than the opponent. BRB p 54.
A steadfast parent unit passes along steadfast to its detachments within 3". Army book p30.
Short, sweet, simple, and consistent.
And we have 7 pages of people turning themselves into knots and handwaving away explicit rules wording in an effort to make up something different...and all you've come up with is that, currently, the parent unit passing along its steadfast rule to detachments
literally does nothing. That's...not very impressive.
Use Occam's razor, folks. It will make your life simpler

Let's use what the rules say instead of hunting and searching high and low for inventions that will allow us to say it means something different.