If you read the GM info carefully it seems that they introduced a new Dex III that was found to be incompatible with PAS systems:
This oil is no longer available so a new version of oil Dexron III has been
specified for the affected ATF (PN 93 160 372, Cat-No. 19 40 712) however
this oil is not compatible with power steering systems and should not be
used for this function because this may result in leakages.
I also recall reading (probably somewhere in TIS - more hope of finding a virgin in a brothel than locating it again!) that it was due to incompatibility with hoses or seals.
Whether that would apply to all Dex III products on the market of just that one specific GM product who can tell? In principle the specs are "backward compatible" but given that PAS fluid really doesn't get worked hard anyway, I'd use Dex II if available and avoid risking it. There's no advantage to using a higher spec fuid (apart from having some left over following a gearbox fluid change).
Kevin