Why do you suppose Benry gave the losties the fake name and the information to prove that it was a ruse (IE - the location of the air balloon). He had to realize that they would find the real Henrys body when they went looking for the balloon and know that he was lying.
So I don't understand why he wouldn't just say that his name was Ben "Smith" and make up a story about a ship wreck that couldn't have been proved or disproved.
It seems that the way he did it was intended to put them in an adversarial position once they discovered that he was, in fact, lying...am I missing something?

I have to admit, I don't know that I'd be digging up a grave, so I think his "story" was spot on so they would accept him as a non-threat. I suppose that if he did bury the real Gale he should've been smart enough to at least take his wallet or license, but that's a minor point. If they found the body and saw it was a gal the game would have been up anyway.

I think it's possible Ben's entire capture was a deliberate plan to gather more information on the Losties. After Ethan's mission failed, Ben may have felt he had to do it himself to get the job done.

He could have also said that that his name is Ben Jones and that he had just gotten away from the OTHERS and was told where they were from ALEX and that he was told that they would keep him safe.

He might not know that Alex was the one to help Claire escape so it might not have been advantageous to announce that she was alive, well, and with them.

if benry (love it!) felt he had to infiltrate the losties (ie if you want something done right, you have to do it yourself), and ben was displeased with the book choice, and he seems to be their leader, does that make him HIM?

Since Ethan failed to get info (or at least that we know of) I think Benry came in his place. I know if I told a fake story to people about a crash and a grave, I wouldn't expect the people to dig up the grave. Maybe he did it to see just how desperate/paranoid they had become?

They want the Losties to be in a constant state of confusion. Instead of using a cover story that in the end would require the Losties to have to take his word for it the extravagant story with a twisted resolution keeps them off balance and turns their focus onto baser issues: confrontation with an evil lying Other that drives a wedge between people rather than "welcome to the club Henry, help us figure some stuff out."