First, let me recommend this link on the two genealogies of Jesus:

http://www.bible.org/qa.asp?topic_id=55&qa_id=61

This article is a short summary, but there are other more detailed ones that I can try and locate if you want. Even so, you'd still come to the conclusion that there is some room for disagreement on this issue.

Now to your question: while it is true that Jesus had no human father, he did have a human mother. This in no way means he was only half-human or half-God, as some religions teach, but fully human and fully God. As such, his physical/ethnic lineage would be through Mary only, but his legal/royal lineage could be through both, according Jewish reckoning.

I don't have the context in which that commentary's statement was made so I can't say what point they wanted to make, but the bottom line is that Jesus had every legal and ethnic right to David's throne; legal because Joseph was his guardian, and ethnic because of Mary being Jewish. This may be partly why God instituted the kinsman/redeemer law for Israel.

At the very least, the commentary's statement, "There is no human bloodline in the body of Christ Jesus", is in error at face value. Mary was human, and a sinner (which brings up the "original sin" issue since Jesus was sinless, but that's for another day). The only way they can claim otherwise is to assume, without any Biblical support, that Mary contributed no genetics at all. But this denies the Bible's clear teaching that Jesus "was made like his brothers in every way, yet was without sin" (Heb. 2:17, 4:15). Also there was no value in his sacrifice for us if he wasn't fully human and fully God.