I can understand their caution since brand X extensions may not fit real well to a brand Y box. They may also be concerned about the length of the wire in the regular box not being long enough.
However, there is nothing in the NEC that I am aware of that would prohibit this & there is nothing in the listing of the extension box that prohibits this.
Have any of the inspectors given you any justification for this practice?
Tom
Few things are harder to put up with than the annoyance of a good example.