This seems like a subtle shift in the discussion.

Just keep in mind what the program is doing: it
applies parameters, resamples the data, and then
estimates the error for that result. When the
minimum error is found, that is the estimated
parameter solution.

But we do not know what the actual solution is.

My previous point was that it is not surprising
or strange for 3dvolreg to get results of 0.01
degrees of rotation or a tiny shift of 0.005 mm.

To this I would append that it does not imply
that your phantom actually rotated or shifted.
The image has noise and distortions that vary
over time. These data corruptions can cause
any program to mis-estimate motion parameters.

- rick