Yes, I skipped every Heroic (I generally play in the wee hours of the morning after work and nobody is online), and I've done all the Bonus Series quests for every planet (when this problem first arose, I went to every planet and every Mission Hub I'd gone through just to make sure). Also, I do my Space dailies because it's quick and worth a bar or so.
I gather it's because I'm lacking crucial combat XP (Bonus parts of quests, etc.) I guess I'm just surprised that Mission XP alone won't carry you.
A screenshot of my current Mission List. I take the Heroic quests and don't track them until I get off-planet