I figured it out.

The denominator inside the parentheses of the basis of the MIRR formula (see MIRR in Excel help) is:

NPV(frate,values(negative))*(1+frate)

If there is only one negative number (initial cost) in the first year (as in the Excel help example), then the above quantity is always equal to the initial cost, regardless of how frate is varied.

The only time varying frate affects MIRR is when there is also a negative number in one of the subsequent years.

This became embarrassingly obvious when I inspected the basic NPV formula:

NPV = Sum[i=1 to n] (values i)/((1+rate)^i)

If there is only one value, then when the above is multiplied by (1+frate), (1+frate) drops out and the result is 'value'.