That idea is one of the most idiotic to come up, and it does
so frequently. And in a number of guises.

The idea being that x.c' <> x.c-vt, with x.c being what
we have called x0 above; the notation makes no difference.

Some crackpots have managed to maintain that position even 
after graphs have illustrated that such an idea means that 
after a while a circle center represented by x.c' could be 
outside the circle. 

The leading crackpot just make that explicit, as far as
one can tell from his befuddled post in response to a line
about "active" transforms, which are actually moving body
situations, not coordinate transformations:
--------------------------------------------------------------------

e>An active transform is not a coordinate transform, ...

 Right, it is a transform of the center (in the opposite direction)
 done to effect the change of coordinates without a coordinate
 transform.  ...

E: Transform of the center?  Center of a circle?
    He really is saying a circle center moves in
    the opposite direction of the circle! Right?
--------------------------------------------------------------------

If r=10 and x.c was at x.c=0, then the points on the circle 
(10,0), (-10,0), (0,10) and (0,-10) could at some time become 
(-10,0), (-30,0), (-20,10), and (-20,-10), but with x.c'=x.c, 
the circle center would be at (0,0) still!  The circle is here 
but its center is way, way over there! Indeed, although a change 
of coordinate systems is not movement of any object described in 
the coordinates, the x.c'=x.c crackpottery is tantamount to the 
circle staying put but the center moving away. Or vice versa.