I'll admit right off the bat to being ignorant of Delaware's laws on the subject.
However, many gun stores have a policy (or at least prefer) that customers who bring guns in to be handled bring them unloaded and cased. Furthermore, the issue of bringing the gun from your car to the store may be distinct from the issue of having it in your car. There is some concern that a gun held in hand might be construed as "brandishing", and if there's no holster the alternative is either a case, or concealed carry, which is illegal without a permit in Delaware.
I'm sure they tell all their customers the same thing. It's not intended to be construed as an opinion of the law, but rather to be a safe suggestion that will never get their customers in legal trouble.
Also, gun store personnel are frequently surprisingly ignorant of the laws not directly pertaining to operating an FFL.
I'm sure other members will chime in about what the laws actually are.