The first part is true. The not using phones from one network to another is not. In some cases. Normally it is a bitch (or flat out not possible) to get all services (sprint tv, vcast, multi media messages, specific network bands) to work though. In this specific situation (iPhone 4s) for a hardware standpoint. Its doable. Most Europe uses AWS spectrum. The verizon 4s is a world phone and can pick up said spectrum (its software locked to not do so stateside). Typically speaking it is pretty evolved and beyond most people's comfort zone to do it though. I am pretty sure you need some special sim card that unlocks it but I am not 100% on that. Back before Verizons big push into global and LTE they only used CDMA. Now with the adoption of LTE and the global market push it's possible and in a some cases fairly easy to get it done... Hell I've let some friends use my ReZound and Bionic on AT&t and T-mobile a couple times.
As with anything else though. Subject to change and individual results may vary.