If you've been eating a nutrient deficient diet for the past month and then the day before you go on a huge tour/hike you eat a good healthy variety of foods that will not instantly make you have super human strength or make you "healthier"
Same goes if you've been eating well for the past month and then the day before a huge tour/hike you don't eat well. The poor food intake the day before isn't going to hurt you.
Diet is a long term thing, not a daily thing. The food you take in over the coarse of months is what determines how healthy and efficient your body runs. It's also what determines your weight. For example, if you eat 4,000 calories in one day, thats not going to make you gain weight. However, if you eat 4,000 calories every day for a few weeks, you will gain weight.
I'm not saying park skiing requires an insanely healthy diet, but a poor diet will help to increase your risk of a deficiency disease. And a deficiency disease can help lead to injuries.