Interesting case. Seems like the police, may have been correct in their interpretation, if it was meant to cover knives, would that mean that you could only carry the long knife if you had your gun on you at the time?
Texas has some horrible knife laws, I once got stopped while driving through Texas, they searched the car, for no reason other than that they claimed I fit the profile of a drug runner, they went so far as to stick a scope into the gas tank and look around, anyway, they found a knife in the back, apparently I was breaking some sort of law about concealed carry, or carry at all, I don't remember, but it was a hunting knife in the back seat of the car, and apparently that's a felony.
They let me go, though, and I learned a lesson about assuming different states have similar laws about weapons.
:edit:
I don't think the police are correct. I think the interpretation that the police are using was probably the intent of the author of the law. That being said, it wasn't written as it was intended.