How a Joule thief works?
It's clearly crap because of the line: -

"will induce a current in the base coil that opposes the currentﬂowing into base of transistor"

That line is self contradictory = crap explanation = untrustworthy site = don't go there!

As an aside, it is voltage that is induced and that voltage produces a current that suits the load (I = V/R). Current cannot be induced into a coil that has no load connected to it or else an infinite voltage will result.

Also, on a joule thief there are two mechanisms that cause oscillation - you have mentioned the saturation of the transistor but, at higher supply voltages it is the saturation of the transformer core that halts the induced voltage on the base coil and thus the oscillator begins the turn-off process.