I believe the "special hardware" in question is either the developer Flash EPROM board or pre-burned updated EPROMs (someone here was selling some recently - I didn't know they could work without the developer board until I saw that post). They're the chips that store the special CDTV programs like the CD player and CD drive drivers. They're separate from the Kickstart chip, and I think, like so much 1.3-era software, they don't work properly with newer Kickstarts. So you might have the Amiga side of the CDTV working with a newer Kickstart, but the CD side components will probably give you trouble until you upgrade the EPROMs.