On minecarts with chests, the lighting applied to the chest is based on the light level of where the player is, not that of the minecart. The minecart part is not affected.

I would expect the minecart and the chest to share the same lighting at the spot where they are located.

To reproduce :
Generate a superflat world, dig to bedrock.
Make a 1 by 2 tunnel under the grass that goes untill it is dark at the end.
Place a rail and a minecart with chest.
Notice both the chest and the minecart are dark.
Walk back towards the entrance of the tunnel you have made.
Notice as you approach the light (assuming it is day) chest gets brighter. The minecart remains dark.

Close of the light from outside to make the entire tunnel dark, the chest is now dark as it should be.
Go back to the minecart with chest and place a torch above it.
Both the chest and the minecart light up.

Back up into the darkness now behind you. The chest begins to dim.