This is the old "physical damage" question and most AHJs have their own opinion of what it really is.
Some places will allow NM on running boards down to some arbitrary height above FF. Others want EMT. Most are somewhere in between (Smurf, MC/AC etc)
It really comes back to how exposed it is to physical damage and is that damage "severe"?
I am one of those middle guys. A metallic cable, Greenfield or smurf would work for most of these cases. I never thought much of Romex on running boards, particularly much below 6'6 but that was the law of the land in Maryland when I was there, down to about 48" or even 36".