"Current is pulled not pushed" they say. Doesn't the transistor working the other way around?
Thinking of current as being pulled versus pushed, or the other way around, is a bad idea.  Such a mental model obscures the physics instead of illuminating it.  Current flows when there is a applied voltage across something, and that something allows the current to flow.

Resistors are very predictable somethings since the current is always proportional to the applied voltage.  The proportionality constant is the resistance (A = V / &Omega;).

Other somethings react differently and are non-linear.  A transistor from collector to emitter is one of these.  The current the device lets thru from collector to emitter is mostly a function of the base to emitter current, once about a volt is applied C-E.  Still, it's the device that allows the current, and can only do so when a voltage is applied to it.