there was a relation in that pid and nature were related and not all natures can have all the different IVs spreads. for example, 31/31/31/31/31/31 can only be modest, calm, docile, and timid. and it's not a hex value, it's pair of rng calls that return a pair of values that are used to create the IVs. they do correspond. if you want simple proof, go play around with SCV's generator. it can take a PID and output possible IV spreads for it.
it's really obvious why not all natures can have all the different IV spread, not a "PID reset" or anything like that. all the natures, abilities, IVs, genders, everything would call for something like 26 billion combos. the 4th gen rng is only 32-bit. see where i'm going? 2^32 = 4294967296 different combos. nowhere close to 26 billion.
e: for DW breeding, if the female has the ability it will be passed to the bred poke 50% of the time.
e2: there's finally NOT a relation between PID/IVs in 5th gen, though. you can catch a poke and change its IVs to literally anything you want and it will still function on random wifi and everywhere else.
e3: no, 4th gen pokes do not have modded PIDs. their 0x41 offset changes to reflect their nature, along with a few other things, but that's about it. the game knows which gen it's from by it's hometown, etc.