Read the help.
movmad computes a moving median absolute deviation.
In no place does it call that a STANDARD DEVIATION. It NEVER claims to prduce a result that is an equivalent standard deviation.
From the help:
"Each element of Y is the local median absolute deviation of the
corresponding values of X inside the window,...
"The median absolute deviation of a vector X is defined as
There is nothing about an estimator of an equivalent standard deviation. movmad computes exactly what it claims to produce. Doing something different than what it claims, even if that is what you want or expect to see, that would be wrong.