What happens if XPS is an inch away from basement walls?
It doesn't make sense to me at all.  Yes adding a one inch gap does add R value as does any dead space - but then why not a 20 inch gap? 

Also I am not sure how you install xps with a one inch gap.  Of course your could add furring strips and then you still have to fire block.  Wow that is just tons of work.

Why would he say that?  I guess he doesn't want the XPS to get wet if you have moisture problems.  Well xps handles moisture just fine and the reason it is often put in basements is that it can get wet, retains very little water, and does not mold (to a point).

The XPS should be on the wall.  You want a "bigger" gap for airflow for the drywall.  Your drywall will mold faster than anything in a basement.  So you want as much space for air to circulate on both sides of this.  Using 2x4 framing gives ample space for small amounts of moisture to dry before it attaches to the drywall and molds.  Would one more inch between XPS and framing help?  I am sure but not sure it is worth the returns which will be very small.