Only O2 barrier PEX should be used in hydronic applications. I believe this explains the situation pretty well:
O2 Barrier vs Non-barrier PEX
The videos on this website may be informative as well:
O2 Barrier vs Non-barrier PEX
Since it is too late to install the proper O2 barrier PEX, you will now need to use bronze or stainless steel components. You will have problems if you don't do this so I don't think there is much value in challenging the inspector about this.
If you don't mind me asking, who sold you a hydronic kit with non-barrier PEX?