They do have an intuitive understanding! You just outlined it, and it works well enough for most things. Statistics is generally very useful, but for individuals it's not really important or useful to understand, because the data is rarely ever clear or trustworthy enough to use for making decisions about specific situations.
Probabilities might be more intuitive, statistics are intuitive only for the most straight forward topics. That's why it's so easy to present entirely correct but very misleading statistics.