I believe that was the case. Dr. Biraj Thakker was our pediatrician for the first couple of days until we discharged our baby from Zydus and moved him under Dr. Anita's care (near Rama Residency). She used to work at Zydus previously and has now moved to Dr. Nayana's new facility. We only interacted with her briefly, but she appeared to be quite competent.
When we had gone to Anand for the first time (2014), many people had their babies under Dr. Anita's care, but I believe that in preparation for the move to the new facility, they had started using Zydus as the default hospital for delivery.
No idea how the new facilities are, but they should be quite comfortable. Yes, from what I heard, it is a "one-stop-shop" and there is accommodation for new parents, but I'm not sure what the pricing is. Also heard that Madhuban Hotel (http://www.madhubhanresortandspa.com/
) caters the food at the new hospital.