Don Woods's answer is correct. When the edges and corners
are in their solved positions, the total face center twist is zero
modulo 180 degrees. Thus the number of face centers that are
twisted 90 degrees must be even. A proof of this appeared in
Cube-Lovers last year.

A process to twist the U face center 180 degrees without
changing anything else is (U LR UU L'R')^2. This process comes from
Singmaster's book. I sent Cube-Lovers a general procedure for
solving the supergroup in January.

If you want a copy of either of these messages, send a note
to Hoey@CMU-10A.