Hi,
As said before: your LED only sees the difference between anode and cathode, and this is what counts.
It doesn't know what "you decided to be GND".
******
Imagine two 9V batteries. Connect them in series.
* Now decide the free "-" to be GND. Now the center point is +9V, and the free "+" is +18V.
* Now decide the center point to be GND. The free "-" now is -9V, and the free "+" is +9V.
* Now decide the free "+" to be GND. Now the center point is at -9V, and the free "-" is at -18V.
... This are just three different decisions, without changing a single connection.
Obviously every single battery is 9V all the time..
Klaus