That is the way I understand it. When I transferred my current boat (KY) they gave me a plate for the trailer. I think it costs a little extra. However I never put it on the trailer and now I don't know where is. I've pulled boats to the north and south borders and beyond and one time I got stopped and questioned about the trailer plate. This was before I was aware it was required if you travel to other states. I replied to the officer "Ky doesn't require a trailer plate" and I guess because that was what I believed at the time I was convincing and that was the end of it.
Best to get a plate if you're going to other states but I think it will cost a little more when you get your annual stickers (not positive on that).