Proper way to enter a median?

I was pulling onto the highway a few minutes ago and pulled onto the left side of the median. A state trooper was apparently nearby and pulled in beside me and motioned to roll down my window, asked me why I did that, to which I had no answer. He told me he could give me a ticket for driving on the wrong side of the road. He then did the typical "pull over" routine, looked at my plate, asked for my license, insurance, etc. He didn't give me a ticket but acted very agitated. So now I'm confused. From what I can find online, nothing dictates a "right" and "wrong side of the median. I've seen my dad do it his entire life, along with people everyday, and I have too ever since I got my license. So is it actually a ticketable offense, or was he just pulling me over so he could look at my papers in hopes he could ticket me for that?