What reps at the store tell you is usually **. The only phone on VZW that is completely unlocked out of the box is the iphone as far as I know. Android phones tend to be both CARRIER-locked and SIM-locked. You need to obtain an unlock code to SIM-unlock your S4, but because of the CARRIER lock that still does not guarantee that a foreign SIM will work unless the carrier has a roaming arrangement with Verizon so that the SIM is recognized. Carrier locking is done so you can't put an AT&T SIM in a verizon phone here in the States even if the phone is SIM-unlocked. Carrier-unlocking in the US without carrier permission is now illegal.
This is a total non-issue in Europe as far as I understand things. They have network-sharing over there and are cutting back on roaming fees, phones are totally unlocked and network inter-operable, tethering is included at no additional charge, and 20 pounds for 300 mins and unlimited data on a caller-pays basis (received texts & calls free) is a fantastic deal compared to the ripoff plans we have here. Ugghh.
Oh, and i forgot to mention in order to get SIMs "VZW recognized" you need to get an international plan added to your account, which of course means extra $$$, The whole thing, like most things in this country, really makes me wrinkle my nose.