Question on BJT operation mode
What you should understand is that the transistor is symmetric about the base.

That being said, the level of doping in the three regions, base, emitter and collector are vastly different. If we consider an n-p-n transistor, the collector and emitter are theoretically interchangeable but current amplification factor popularly denoted by beta is high, about 50 - 300 for an average transistor in the active mode and much lesser, about 0.1 - 2 in the reverse active mode. This is decided by the level of doping in the different regions. 

In active mode, B>E for forward bias and C>B for reverse bias, hence C>>E. Similarly in reverse active mode, B>C for forward bias and E>B for reverse bias, hence E>>C. So yes, all your sources including your professor and your textbook are correct.