I agree with you seawench. But I don't just think it's the cruise lines that think a 4-inch step is "no problem". This misconception exists throughout the tourism industry. In fact many people thing that everybody who uses a wheelchair can get up and walk a few steps (probably because they saw someone do it once).
The bottom lines is that there is very little accessible transportation in the Caribbean (even the locals have a hard time). It really doesn't matter how new the ship is, you are still only going to find the same (limited) accessibility in the Caribbean. So it's just a matter of putting together your own shore excursions and making do with what the islands have to offer, because the crusie lines really don't offer much in that dept.
Editor, Emerging Horizons
The only accessible travel magazine.
***edited to remove commercial link***