Jacko said that small ligament tears can heal, but thats a little misleading. Ligaments have a very poor blood supply, so no new ligament tissue is formed, unlike, for example, bones. Ligaments "heal" with scar tissue (" In fact, evidence suggests that the injured ligament structure is replaced with tissue that is grossly, histologically, biochemically, and biomechanically similar to scar tissue.") Scar tissue does not function like a ligament, so its more that the player will need to adapt to the new biomechanics caused by the injury "healing" in the absence of replacing the ligament with surgery. Although scar tissue and ligaments are both made mostly of collagen ligaments are composed of type 1 collagen, which is more densely packed, stiffer, and stronger than the type 3 collagen in scar tissue. Bottom line: ligaments "heal" but there is generally a persistent change in joint load bearing ability due to scarring.
What is going on with Price is a bit mysterious. Clearly we are not being told the whole story.