The easiest way I know to prove this and test since you likely have the switch out of the layout- use a 9V battery between center rail and outer rail at the diverging entrance of the switch. Only use the battery if the switch is completely disconnected from your track layout and any power source. One polarity- say center rail positive, will light the white indicator at the switch and one of the 2 color states at the remote control (you have to switch t both straight and then out to show both possible states). However, the reverse polarity- center negative, the white LED is not lit, the remote control stand can light the other color when the switch is in that state, but then no lights at all in the other direction.
It's also possible they got the polarity of the 2 contacts for the white LED reversed, which again, with AC works, but with DC power source, may not work for a given polarity.
We get this locally a lot because people buy the Lionchief starter set with DC power pack, then begin expanding, buying switches, and then complain the new remote fastrack switch is bad. Then we have to demonstrate to them that their switch is not bad at the store, and they need to upgrade to AC power for the switch indicators to work as intended.