Narrow inner borders are primarily used to achieve one of two goals: (1) to create a 'dead stop' between the center pattern and an outer border, and (2) to adjust the measurements of the center section so that a pieced outer border (like your Delectable Mountains) fits accurately (a coping border). In your case, it is the pattern repeat of the outer border that should determine whether an inner border should be added, and, if needed, how wide it should be.
With your Delectable Mountains, does the spacing of that pattern match up with the measurements of the center without an inner border? If not, how much larger does it need to be for an even repeat of the mountains? Half that measurement will be the width of the inner border. If it does match up without an added border, you'll have to decide if you want to increase it by a full repeat of the width of the mountains. In that case, the inner border would be half the width of the mountain repeat. Hope that makes sense.
I would certainly not add a narrow inner border just because you think you're "supposed to" for some reason...especially if it messes up your spacing in the outer one.