PaulS:
No, it doesn't. It means that the LED has power. Do NOT read more into it than that.
But the LED glows only when the sensor detects something. It is directly connected to the sensor output and nothing else. The sensor has its own LED indicator as well.
I just tried this again by replacing the sensor with a limit switch. The new setup works fine.
The only thing strange with the sensor was that its analog output continuously fluctuated between 0 and 1023.