And they can. For physical injury. Those exceptions are stated in the rules, which @vreddy posted.
Giving an exception that is NOT in the rules would amount to making special rules specifically for Osaka.
In other words, I don't see anything wrong with what the Grand Slam committees have done. Osaka and her team, especially PR, on the other hand have bungled this. If they thought that she was such huge super star that the Grand Slams would bow to her, well, they thought wrong.
Btw, most of the support Osaka seems to be getting is from other celebrities, who are likely worried it might be their turn soon. The common person who doesn't have the money or clout is hard pressed to feel sorry for mega millionaires whining about their problems when they themselves have to do things that are difficult and unpleasant just to earn a modest paycheck, and don't have the luxury to get any attention for their afflictions. Their thinking is "I'm struggling and no one cuts me any slack, why is this prima donna queen demanding special treatment. Suck it up and do your job like I am. Or take a break. Or quit."