I see a bit of confusion here, and it seems to be caused by semantics.  People can argue forever over whether the transistor is "voltage controlled" or "current controlled."  And each side means something different by that.  And each side is trying to win an argument, not trying to clarify matters.  (They already know the truth.  In any religious battle, the first rule is to never question the viewpoint you're defending.)

 Instead, what if we ask a different question:  how do transistors work?

 In explaining the transistor effect, if we drill down through various ideas, we find a central concept:  when the base terminal injects charged particles into the base region, there is no way for the motion of those particles to influence the other charged particles being sent out by the emitter.  There is no mechanism by which the base charge-flow can directly affect the emitter's charge-flow.   Yet if we inject a tiny base current, we obtain a huge emitter current!  The hfe parameter is no illusion.  Base current obviously does control emitter current.  How?  It's because any change in Ib absolutely requires a change in Vbe... and Ie is determined by Vbe because Vbe determines the thickness of the depletion layer.   Base current can control emitter current through a multi-step process involving Vbe and the depletion layer.  Charged particles injected by the base do in fact influence the charged particles sent out by the emitter.  They just can't do it directly.

 So is a transistor controlled by current?  Yes, if by "controlled," we mean that the emitter current can be changed by changing the base current.  Is it "controlled" by voltage?  Yes, if by "controlled" we mean that the emitter current can be changed by changing the value of Vbe.  And those people who choose one side or the other can fight forever about the "right answer."  They'll almost come to blows over the One True Path to transistor enlightenment, since their own viewpoint is obviously good and true and right, while the opposing side are all a bunch of worshippers of Darkness and Confusion whose blasphemy must be ridiculed.  After all, young students could be misled from the One True Path!  Think of the children!  )

 On the other hand, it's hard to become a victim of either meme if you laugh at religious wars.  But that's a very difficult habit to develop.  Instead, it's easier to become a devout "Current Believer" at the start.  But then the mental grip of that meme is shattered by encountering the competition.  So you become an outspoken "Voltage Worshipper."  With luck you'll eventually be immunized against both, yet accept both.  The "Transistor Zen" practitioner is free to view BJTs from both viewpoints, switching back and forth as needed, while seeing the duality as an illusion and rejecting the notion that a single best answer can exist.