Burning a Atmega 328 Bootloader with an Arduino Leonardo

Look carefully at the signatures array: it has entries that are completely initialized and there are ones for which the bootloader and subsequent fields are left uninitialized (in which case they are guaranteed to be all zero's).

You modified an entry of the second type: one without bootloader support.
More precisely the ATmega324P entry. But you have a 328PU. So I think you were lucky it did not write anything, if it had written incorrect fuses, the chip could become unrecoverable for ArduinoISP.

I would create a new entry in the table by copying the one for 328P. But consult the datasheet for the AT328PU and check wether the fuse settings are correct (for the crystal you wish to use).