SmartThings does use ZigBee and Z-wave standards for much of there things. I have at least 20 Z-wave devices in my house used with SmartThings.
The Hub can connect to these things locally… but the Hub is just a communication pathway. It is rather “stupid.” The Hub doesn’t make decisions, it just repeats stuff. When a z-wave device send info to the Hub, the hub just repeats this info to the SmartThings cloud. When the cloud wants to turn a device on or off, it sends the command to the Hub, which just repeats it to the specified device.
All the decision making, all the brains of the system, sits in the SmartThings cloud server. If you don’t have an Internet Connect the cloud can’t tell the Hub what to do. The Hub is too “stupid” to know what to do by itself.