No, I believe you're conflating the principal place of activity with the registered agent -- they do not have to be the same.
The registered agent is responsible for getting served, receiving legal mail, and other government correspondence on behalf of the company and forwarding it along in a timely manner.
This is different than a mailing address because a process server or government employee must be able to physically walk into the premises of either the principal place of activity or registered agent, deliver the notice/correspondence/etc. to someone, and record who they handed it off to at what time.