Is this negative regulator really meant to be an inverted positive regulator?
What you have shown in the yellow box is OK, because the 18&nbsp;V secondary that's sourcing the 7815 is fully isolated from the other rails. This means the 15&nbsp;V output is fully floating, and any terminal can be grounded.

If you want to use a centre-tapped transformer (with some slight savings in hardware and diode drops) which produces non-isolated rails, or the non-isolated rails from another piece of equipment, then you need to use 79xx series regulators for the negative rails.

The reversed 7815 you've drawn will not provide the -15&nbsp;V you want.