You are in the right - you do not need to say you are on own nav to pointABC.
Even if you are on a heading, you technically do not need to report that to the next agency unless told by the previous controller. The reason controllers tell you to report heading/speed is because it is a legitimate, laid down method of not having to make a phone call.
Good airmanship however would involve telling the next controller if you were on a radar heading, regardless of whether you had been instructed to report it.
Sounds like the controller(s) in question were having a bad couple of days