In Rustyspoon's scenario, this summing amp would not work because it functions just as a mixer and if you examine the three inputs, they are summed (merged, mixed) with no way to mute two inputs to hear one or to then switch to another input.
As others have pointed out, passive signal splitters don't isolate the signals from each either, they mix the input signals into a single output.
The Behringer headphone amp is not a mixer. The two inputs are discrete and isolated from each other and only one input can be selected at a time. A user selects which input to feed the headphones with a push button switch. The two signals are not internally mixed and the signal level can be controlled from the source or the headphone amp.
According to the video Misha posted, the Pokket DJ Mixer can select between left and right input or mix between the two. It's the best of both worlds.