I am not suggest base voltage has no influence, just not an "accurate" influence. The relationship between current and voltage through a resistor in a simple circuit would be an "accurate" influence. We do not have that relationship between the base and collector of a transistor since there are two circuits involved, base circuit and collector circuit. If we have no collector load base voltage and current can change but collector current does not.hp1729are you trying to say that the Vbe has no influance on collector current ?

How can you explain the working principle of a BJT current mirror without involving Vbe then? We can ask the same question about differential amplifier.

I think we would have to put this in context of the original text to realize what the author had in mind.