I was thinking about this a lot. I agree that is is obvious that an area which is homogenous in VV can also be heterogenous or even completely different in VH. But to my understanding this only affects the intensity of the filter.
If an area is homogenous throughout a stack the filter considers all the variation as speckle and therefore is more rigorous.
If it is different throughout a stack (maybe due to temporal changes or different polarizations) the filtered result is less smoothed but not necessarily wrong.
I made a few tests and didn’t find that a pattern from one image is transposed or ‘copied’ into the others during the multi-temporal filtering.
How do you think larger errors could occur?