Nobody is saying that a mitzva tantz is not the mitzva of keitzad merakdim. All we are saying is that the particulars which make it unique are not from the machzor vitri.
As such, those particulars do not have that source. They probably have some source, but it is probably not 1000 years old. (This is not something which should bother chassidim; none of their unique minhagim are very old.)