No explanation needed. It's a moot point in the comic/cartoon world. Anybody who's watched a massive,hulking Megatron in the cartoons transform into a pistol small enough to hold in your hand knows this.
Sheesh.

Wolverine without adamantium would eventually grow new legs. Wolverine with adamantium only needs attach the two pieces of his spine together, preferably while combining his fleshy parts as well. While adamantium-Wolverine can't grow bones, he can grow ligaments and other directly "non-bone" materials. Which will eventually make the connection between the bones. And the healing factor will eventually correct any adjustment error he might make while connecting his spine.

Or he'll be walking kinda funny for awhile after that.