Yes, that is correct.
Copied from an old topic:
The quest log has a section for open quests, and one for completed quests; side quest names are listed in white text, with main quest names in gold. If you have completed the conditions for a quest but not turned it in yet, or it is a recurring quest (Hearttaker), the name will be shown in the open quest section in green text (after turning in some goblin hearts, that quest will revert to white and remain in the open quest section). If you fail a quest, or for any open quests in Broken Valley or Sentinel Island when you take the battle tower (except one quest in each area that must be left until later), the names will be shown in the completed quest section in red text.
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