I think they're daily reset, at 3am EST (midnight /servertime) (like all other quests), so if you completed the skirm after that it counts as a completion for the next day..
Also are we even sure the skirmish loot is skirm-specific? We have not run Gondamon raid but I have that Brown Wizard's Band too. I forget from which though, either Attack at Dawn (which doesn't have Sup 4th mark raid quest!) or Trouble in Tuck, I think...
Also have a Careworn Earring from some unknown raid skirmish, which is 92 will/61 vit/332 outgoing healing rating/332 tactical offense rating. At work so no pic.
I got this same item from a Prancing Pony raid - so probably any that share the same campaign mark?
edit: Just read that page, doh! Nevermind the above.