A bridge rectifier being fed with AC or either polarity of DC will always output a fixed polarity of DC on the output +/- terminals. Given that fact, if you have an unknown source of power, a bridge rectifier will turn it into DC with a polarity you can count on.
FYI, most TMCC stuff outputs half/wave track power in command mode, the LCRU just happens to not control which half wave side it puts out, it's random.