I think he meant they were looking for ANY privateers, rather than citizens specifically.
However, the very fact that "citizens" are INCLUDED as a sub-set of "privateers", who could be from other places, means surely it was OK for our own citizens to have "big arms"/ordnance.
I think we are getting side-tracked. The intent of the 2nd Amendment (as I read it) was to 1) provide a necessary institution (the militia) for national security and 2) to prevent the government from disarming the people (who make up the militia). What does a militia do from a constitutional perspective? 1) It defends us from foreign invasion 2) it ensures the enforcement of our laws and 3) provides an offsetting power to the government's army in the event that the government should endanger our liberties. Whatever weapons needed to perform those missions are what is protected (simple analysis, I know, but logical and I believe faithful to the historical meaning of the BOR).