That is not entirely true.
What you describe only covers the transportation of a pistol and ammunition. However, your possession is still not justified. You will be at risk if caught.
You are only allowed to transport a firearm into the Sheeples Socialistic Commonwealth of New Jerseykstan for purposes of "legal use" (target practice at a licensed shooting range, hunting, etc.). And, you must proceed directly to the place of legal use and leave immediately afterward, along a reasonably direct route making only such deviations as are "reasonably necessary." I fear that most NJ persecutors would not consider attending a USCG graduation to be a "reasonably necessary" deviation.
We just could not abide someone like you coming into our great State and possibly shooting one of our criminals.