We've only heard one side of the story. I know that's plenty in the O'club but it's still only one side and certain to be slanted towards the person providing the story.
Just a couple points here. In AZ. and some other states, "willful concealment" is sufficient for shoplifting. That means putting the package beneath your clothing, consuming the product before paying or hiding the item in a place for later retrieval. Almost all stores will wait until the suspect has bypassed the register before attempting to stop. The suspect does not have to get out of the door before being detained.
The receipt check annoys the hell out of me too in place like Best Buy and even wallyworld. I've refused to stop, particularly when the individual has just seen me go through the register and pay for all of the items in the bag. from just a few feet away.
If, and I say IF, the guys story is true in the blog then the store folks are looking at an unlawful imprisonment situation and a law suit as long as all they have is a failure to produce receipt or allow inspection of the contents and no other indication or proof of theft. There are times to pick and choose your fights, and this one shouldn't have gone that far if that was ALL they had. There would have been no reasonable suspicion of a crime in that case.
As far as failure to ID to a Police Officer is concerned. You are required to provide sufficient information to establish your identification. That means a picture ID with name, DOB, address etc. on it or to verbally provide that info. If this guy merely provided his name he didn't comply with the requirement. In that case the arrest will likely stand if the prosecutor doesn't drop it because they don't want to deal with it. All the Officer had at this point was a possible shoplifting, depending on what the store personnel told him.
If it had been me responding and all they had was a refusal to show receipt with no other indication of shoplifting I'd have stopped right there after getting the ID info from the guy. A name, address and comparison from the license plate would have been sufficient as there was no basis for an arrest or stop by store employees in the first place. It would now be a civil problem between the store and the individual.