As far as I know, the cause of PPHN is unknown. If the doctor was implying that the location of your birth canal (home, not hospital) during the baby's birth in some way caused the PPHN, he is quite incorrect. Some babies just come out and their circulatory systems just don't make the switch. It sucks, but it couldn't have been caused by the location of your birth.
You didn't need to induce, because you went into labour! That's what you say when people ask. Induction is for when you don't go into labour. But you did. Jeez, it's like they're idiots over there.
This was not your fault. The PPHN would have happened if you gave birth in the hospital too. This doctor is an insensitive, narrow-minded jerk, and I'm so sorry that he said that to you about your precious baby and your lovingly chosen home birth. It is your right to "fire" this doctor, if you wish. I had to fire one after he refused to listen to me when I said something was amiss with my baby (guess who turned out to be right...) A doctor that's too attached to his ideology and sense of superiority is not one I want making choices about my child's critical care.
OB RN, partner to and mama to (2008, 31 weeker) and (2011)
BTW, I don't homebirth but I have known plenty of hospital born babies that have had the same issue. That doctor was outta line.