Any recommendation depends on your location - I wouldn't provide the same answer for Yuma, AZ as I might for Edmonton, AB.
When water vapor diffuses through a wall and reaches the exterior sheathing, if that sheathing temperature is below the dew point the vapor will condense. Depending on the amount of water vapor and the rate at which the wall cavity is able to dry out, this may lead to moisture problems.
Installing insulation in the wall cavity will help reduce heating costs, but won't address the problem of sheathing temperature. As a result, some builders are specifying 2" to 4" or more foil faced polyiso panels be installed outside of the sheathing to raise the temperature above the dew point. In these designs, some don't even advocate using cavity insulation. Vapor will still diffuse into the cavity, but it will not condense on the sheathing surface.
Installing foil faced polyiso on the interior of the wall, properly air sealed and with taped joints, forms an effective vapor barrier which will reduce the problem of moisture diffusing through the walls. However it may not solve all of the problems with vapor diffusion so it's quite possible to still have problems.
Additionally, while most people look to insulation as a primary solution for energy savings, often older homes would find greater benefit from air sealing. There is almost no way you can make an older house with plaster walls "too tight." In fact, the idea of houses being "too tight" is something of a myth. Your goal should be to have "managed ventilation" rather than the unmanaged ventilation common in older homes.
In my 1870's New England house as an "inside" solution I removed the plaster, installed fiberglass batt insulation in the cavities, applied 2" foil faced polyiso over the studs (for a thermal break and vapor barrier), with 1x3 furring strips and gypsum on top.
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.
Best Answer
Google 'wet spray cellulose insulation'. You'll see videos etc where they spray messy then scrape flat. The kind folks at HD obviously had helpers scraping (and cleaning up the guy doing the application...)