He's correct.
From: The New Testament - A Historical Introduction to the Early Christian Writings. 3rd. edition, Bart D. Ehrman, 2004, Oxford University Press
pg. 121
What is striking, however is that Joseph's ties to David are traced through different lines in the two accounts. In Matthew, Joseph is a direct descendant (from father to son) of David's son Solomon; in Luke he is descended through a different line, from David's other son Nathan. The discrepancy can best be seen by moving backward through the genealogy, beginning from Joseph. Who was Joseph's father? Was is Jacob (as in Matthew) or Heli (as in Luke?). Was his paternal grandfather Matthan or Matthat? Was his paternal great-grandfather Eleazar or Levi? His great-great-grandfather Eliud or Melchi? And so forth. One of the fascinating aspects of scholarship is to see how readers have attempted to explain these differences over the years. Some have claimed, for instance, that one of the genealogies is Joseph's and the other is Mary's. The problem, of course, is that both of them explicitly trace the ancestry of Joseph (Matt 1:16, Luke 3:23).