if it isn't easy, how can Shop Pad turn it on or off so easily?
They would have built a chunk of code that sits on their own servers to emulate a form of mobile view. Essentially hosting a mobile theme that you're redirected to if certain conditions are met. It seems to work ok. As for why it's simple to turn on and off - liken it the to engine of the car. The ignition is a simple toggle of code. It's making the engine (the bit you want) that's the hard part.
I never said I wanted it integrated with my current desktop theme
Unless you get your account on that legacy account to use mobile themes you do need to integrate the code with your current theme. Even if only on superficial level - it must still co-exist (unless you go down the app path).