First off, those guys are douches. Palmer makes great boards. I have an 07/08 Honeycomb 4. That board doesn't look like any of the honeycombs I've seen, but then again, Palmer's been making them since 97. And as far as regular vs. x honeycomb, never heard of that.
The honeycomb is made of Nomex, made by DuPont, it's aramid (similar to Kevlar). Very stiff, very light. Nomex is usually used in high temp applications, like race car driver suits. Nomex, like Kevlar, is also very strong and can take a lot of compressions. The core is mainly air. There are actually wood stringers in the middle to add pop, Bubinga I think, an exotic wood from Africa. The honeycomb is 99% air, but the core itself is something like 90% air (because of the wood). Nomex honeycomb is synthetic and won't break down as quickly as wood, and won't corrode like Aluminum. Aluminum also dents easier but is encapsulated so there shouldn't be any concern with corrosion.
Honeycomb itself, is just a pattern of structure made of hexagonal cells, like a bees nest. This structure is great and used quite often in the aerospace industry (I used to work on fighters for the Air Force.) Honeycomb is strong, resilient, and its pattern transfers forces or energy throughout the board. Honeycomb is great against impact along its edges, but suffers more from impacts of compression. Meaning, if you run into something like a tree, it should hold up well. But if you drop something heavy onto it, not to much.
Elan, Nidecker, Burton, and Palmer use honeycomb in top end super light boards because its a great structure.
The board in the pic isn't any of the Honeycomb IIIs or IVs, IV (4) being the current revision. So, if it is a Honeycomb, it must be old. The douches need to read a book.