You don't really have to go into a lot of scientific detail at that age unless you really want to. The information she was given was pretty simplistic, so all you really need to do is explain that your family has different beliefs and explain why. At the most basic level you can talk about how the way food is produced/grown makes a big difference in how many nutrients it has and we want to fill our tummies with foods that have lots of nutrients to keep us strong and healthy instead of processed food that fills us up without giving us the nutrients we need to live and grow. One of the ways we know which foods are best for us is by looking at the foods our ancestors ate many, many years ago and making sure we are also eating plenty of those foods. Calories aren't bad or good. They are simply a measure of energy. It's not as important to think about calories as it is to choose healthy whole foods like fruits, veggies, meats, and fish.
You can also explain how for a long time people thought that eating fat would make you fat, but we now know that isn't true even though some people still believe it. There are some fats that are unhealthy to eat (manufactured transfats, industrial seed oils, etc.), so your family doesn't eat them.
If you want to get into more detail, there are some great teaching resources designed for kids and young adults. While not specifically paleo, the Omnivores' Dilemma has a kids' edition which explains the problems with factory farming and emphasizes the importance of eating whole foods. Food Renegade has two nutrition programs for kids. One is for ages 6-11 and the other is for teens and adults ages 12 and up. Again, it's not specifically paleo. It follows the WAPF philosophy, but it is still going to be pretty close in line with paleo beliefs. You can always skip the dairy (if you avoid dairy) and grain/legume chapters.
One more thing: your child is likely going to wonder why the teacher gave her bad information. I would definitely make sure you take the time to explain that the teacher isn't "lying"; s/he believes the information will help the students. Explain that different people, and even the government, have different beliefs about nutrition and because there are so many different theories it can be very confusing for people. But, you have spent a lot of time reading about nutrition and you believe this is the best way for your family to eat to stay strong and healthy.