Did Luke Just Carelessly Accept What Matthew Said About The Bethlehem Birthplace?

Here's a podcast from a few years ago in which a New Testament scholar, Mark Goodacre, discusses why he doubts that Jesus was born in Bethlehem. It's about ten minutes long.

Notice how much evidence he ignores. He doesn't even address one of the significant points made in the N.T. Wright clip that he plays. As Wright notes, there would have been widespread interest in and knowledge about Jesus' birthplace. Thus, the idea that everybody would have been dependent on Matthew, or one source used by Matthew, for that information is dubious. Jesus' brother James was a prominent church leader for a few decades, for example. He never commented on Jesus' birthplace? Or he did, but Christians didn't have much interest in what he said? What about other relatives of Jesus who were prominent in the early church? And so on. Besides, if Luke considered Matthew trustworthy enough to use his information on the subject of Jesus' birthplace, doesn't that suggest that people like Goodcare need a better reason for dismissing Matthew's testimony? Arguing that Luke was dependent on Matthew isn’t enough. Luke's gospel opens with references to his interest in investigating his material (Luke 1:1-4), and he had access to individuals who were in a good position to provide reliable information on Jesus' childhood, like his siblings (Acts 21:18, 1 Corinthians 9:5). Much of Luke's material on Jesus' infancy isn't found in Matthew's gospel. If Luke did that much research to come up with so much non-Matthean material on Jesus' childhood, are we to believe that in the process he never came across any sources on Jesus' birthplace that were independent of Matthew?