Two things.
One, the GRE is largely a reasoning test. The two multiple-choice sections are called Verbal Reasoning and Quantitative Reasoning. They want to know about your reasoning ability - your ability to solve problems and think logically. They don’t care whether you know the distance formula, either; what they DO care about is whether you can use your wits and knowledge to answer the questions correctly. I don’t remember the distance formula either, but if you gave me two points on a plane, I could find the distance between them by deriving the formula given what I know about basic algebra and geometry.
That’s why the questions are really only up to like 10th grade level math; they are less concerned with the breadth of your mathematical knowledge than they are with your problem-solving skills. Similarly with the verbal section - they want to make sure that you have verbal facility that enables you to read graduate-level texts. You don’t actually have to memorize all of those GRE words; you just have to be really good at figuring out what words mean in context, and how to extract meaning from a boring passage.
There are a few basic stats questions on the GRE - they are called “data analysis” type questions.
Data analysis topics include basic descriptive statistics, such as mean, median, mode, range, standard deviation, interquartile range, quartiles and percentiles; interpretation of data in tables and graphs, such as line graphs, bar graphs, circle graphs, boxplots, scatterplots and frequency distributions; elementary probability, such as probabilities of compound events and independent events; random variables and probability distributions, including normal distributions; and counting methods, such as combinations, permutations and Venn diagrams. These topics are typically taught in high school algebra courses or introductory statistics courses. Inferential statistics is not tested.
But in order to do complex statistical analyses you need to know basic math - algebra and geometry. So if you can do the very basic, high-school level math on the GRE then you are prepared to learn the higher-level statistical stuff you need for data analysis. Conversely, professors may reason, if you can’t even do the basic math on the GRE how will you be able to perform the high-level stuff?
Remember that the GRE is a general test, designed to be administered to students in all kinds of fields - from English literature and history to physics and mathematics. If quantitative facility doesn’t matter in your field (as it would not in literature or history), then you probably don’t need to worry too much about your quantitative score. If verbal facility is less important (as it might be in physics and math), then you wouldn’t need to worry so much about that section. If you are in a social science, though, I would say that quant matters at least a little (except perhaps for anthro, and even then it depends on the kind of anthro and the specific department).