Step 1: Locate the structure. The iliolumbar ligament is a stout band stretching from the tip of the L5 transverse process to the inner lip of the iliac crest behind.
Step 2: Restate its anatomy. Its upper fibres anchor onto the iliac crest, its lower fibres reach the base of the sacrum, and overall it braces the lumbosacral junction against shearing forces.
Step 3: Check each claim. The statements about iliac-crest attachment, sacral attachment, and lumbosacral stability all match the true anatomy.
Step 4: Catch the error. The ligament springs from the transverse process of L5, not from T12, so claiming a T12 origin is incorrect. That false statement is the answer.
\[\boxed{\text{Upper attachment to transverse process of T12}}\]