My experience with rims with less than a 14mm inner diameter has been negligible and my understanding is that not many clincher rims are available that are much narrower than that. I stated "extra narrow" followed by a qualifying measurement of 14mm - I would personally consider anything less than that to be "extra narrow."

I have a lot of experience going downhill and cornering on 14mm ID rims with 1 1/4" or 32mm tires and I can tell you from experience that at speed it is possible to feel the sensation of them deforming over the lip of a narrow rim, which is something that is not experienced on the same rims with more narrow tires. Hence the point I shared above about stability and steering control. As I mentioned, I don't see any safety concern as far as the tire actually rolling off of the rim, but a wider rim under a 32mm tire would certainly offer more support and less tire deflection, or vice versa.

Here's a handy chart from Sheldon Brown that I know many people would say does not paint the full picture because there are so many considerations about the quality of the rims and tires. However, it gets a point across that I firmly believe, which is that there are ideal combinations both from the perspective of safety and performance:


Tire Sizing Systems

-Gregory