The reason why you're not supposed to put hot food into the refrigerator is because the hot food is supposed to keep the refrigerator warm and not allow the food to cool down properly soon enough to prevent bacteria growing on the food.
And it's recommended to leave the food out at room temperature until it cools down but that doesn't make any sense either because when you leave it out the food is still able to grow bacteria and it will just take longer to cool down.
I've put hot food into the refrigerator before and never has it been a problem nor have I or anyone else gotten sick from doing so.
The hot food is not gonna hurt the refrigerator either as it will just run a bit longer to start cooling the refrigerator back down once it begins to warm up inside.
So bacteria will not grow on the food when you put it in the refrigerator.