After doing some digging:

  • http://www.xbox360achievements.org/forum/showthread.php?t=386051
  • http://www.gamefaqs.com/boards/615803-/63954526

It turns out the glitch is caused by completing the Dark Brotherhood quest - Kill Helvard.

Apparently, the Jarl of Falkreath knows you killed Helvard (even if you are sneaky about it). In fact, I killed Helvard when he was taking a nap, so Helvard certainly didn't see it coming.

Anyway, after killing the Jarl's housecarl, Siddgeir's disposition is lowered significantly. Since I am already Thane in Falkreath, there is no way to raise his disposition, unless I was playing the game on PC.

However, I fortunately found a solution! If you have NOT completed any of the Legion/Stormcloak quests, then make sure to do the following:

  • Side with the Stormcloaks so Dengeir replaces Siddgeir as Jarl.
  • Talk with Jarl Dengeir (he will ask you to become Thane again)
  • Talk with Tekla, the newly appointed steward, and she will give you the option to buy land

I really hope this helps someone in the future!