To be clear, clubs getting a charter has nothing to do with flying sites. Lots of clubs have no flying site, some have multiple. What it will effect is getting an insurance certificate for the land owner.

And it is correct, the FCC has not rules that directly effect the 3 mile rule. However, they do have a rule about malicious interference. So if you know there is a field and you fly close enough to cause an issue then it is possible that you could be caught by that rule.