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IMO, any athlete who competes is the arbiter of what goes on in their body and how much they can take, even if it may cause future damage, or even it that damage is debilitating.

Women are at a disadvantage because of their biology and structure, and is primarily why nearly every physical competition is segregated by sex in a fair environment. The US military, when it was considering whether women should be included in direct combat units USMC Veteran Jude Eden wrote this in her excellent article "Women in Combat: The Question of Standards:

In his 2013 book Deadly Consequences: How Cowards Are Pushing Women Into Combat, retired Army Col. Robert Maginnis describes several military studies showing the physical suffering of women in combat:

A U.S. Navy study found the risk of anterior cruciate ligament injury associated with military training is almost ten times higher for women than for men.
A sex-blind study by the British military found that women were injured 7.5 times moreoften than men while training to the same standards.
Women suffer twice as many lower-extremity injuries as men, an Army study found, and they fatigue much more quickly because of the difference in “size of muscle,” which makes them more vulnerable to non-battle injury.

Marine Capt. Katie Petronio, writing in the Marine Corps Gazette about Officer Candidate School, states: Of candidates who were dropped from training because they were injured or not physically qualified, females were breaking at a much higher rate than males, 14 percent versus 4 percent. The same trends were seen at TBS [The Basic School] in 2011; the attrition rate for females was 13 percent versus 5 percent for males, and 5 percent of females werefound not physically qualified compared with 1 percent of males.

Lindsey Vonn was within her individual rights to push as hard as she thinks she can. It is up to the coach of the team to consider if that is wise to let her proceed. And they deferred to her because of who she was.