Newbie - What is the Difference Between Power Supply's GND and Arduino's GND?
I would expect there to be no difference between the grounds in your circuit, and after looking over the schematic for the board, it appears that all of the grounds are common.

I think the most likely explanation for what you're seeing is a quirk in the breadboard. It may be that the side busses are split at the middle of the board, or perhaps there was just a bad connection somewhere on the ground bus on that side of the board.

One way you could troubleshoot it further would be by jumping the ground side of the LED to the power supply ground. Start with the ground on the regulator and then work out until you find the spot where you loose continuity.