I'm in the exact same situation, have been for years. The traspaso was originally done by someone we know and we had no part in it aside from payment. I just checked in the system online at DGII, with the number of a cedula that is not mine and our placa, my name pops up perfectly fine. Not even spelled incorrectly or missing parts. When the traspaso was done, they had my passport (back then it was done with passport), but the new matricula came with a number of cedula (not mine) and I asked why, the answer was exactly why you state above, "no clue" and does not matter.