The PZ parolee is by definition reformed and therefore no longer a criminal, I think, and therefore can claim ownership of their heritage.
True, but there are limitations for convicted criminals even in the most progressive societies and it is hard to imagine Krypton being different.
Sure, a Phantom Zoner may be reformed, but that doesn't necessarily mean that they should be given access to Blizzard Rays, just like in our own society paroled criminals cannot associate with known criminals, cannot own a firearm, and so forth.
Even though something is Kryptonian, it would not be unreasonable for Superman to say "okay, all this stuff that can potentially blow up the earth? Nobody is touching that."