As Darknight points out, the wording still isn't a 100% clear (surprise, surprise). I agree that according to the FAQ the parent does not need to be in combat itself. However, as he also points out, it does seem that if the Regiment is in close combat and as a result is not steadfast itself, then the Detachment cannot be steadfast either, even if it would be steadfast on its own merit.
I guess, GW still has not thought this through.
@ Commandant: what Darknight says. Both main camps obviously held that for the Detachment to be steadfast, the Regimental Unit had to be steadfast in the first place.