Yes, it's a multi-layer board and that ground wire on the cap is probably connected to the internal ground plane of the circuit board. That's why it's so hard to desolder. You have to heat a lot of copper to get the solder hot enough to melt.

Try a higher temperature setting or apply the heat for longer. Don't force anything. You don't want to pull the grommet out of the via. But it's going to take more heat to make that big ol' ground plane let go of that lead.

There's really no harm in the "bodge" you've done anyway. It may not look very neat, but it is electrically sound. I did a similar thing with the fuse in the Apple 14" Color Plus Display.