Is a transistor truly an amplifier?
amplify
/ˈamplɪfʌɪ/
transitive verb

to expand (something, such as a statement) by the use of detail or illustration or by closer analysis
a: to make larger or greater (as in amount, importance, or intensity) : INCREASE
b: to increase the strength or amount of
especially : to make louder
c: to cause (a gene or DNA sequence) to undergo amplification

Source: Merriam-Webster.

Sure it does dictate when the huge current can or can't flow but it is doesn't change the huge current in any way I think.

It sounds as though you are thinking of a transistor as a switch where it is either fully on or fully off. Many applications use it as a controllable element where it is partially on. In these cases, the base is used to control the conductance of the collector-emitter terminals and hence it controls the current in an analog manner. This fits the dictionary definition 2 above. The fact that it is controlling the amplitude of the current means that it is changing it.

Figure 1. From Horowitz and Hill, The Art of Electronics. &quot;Transistor Man&quot; looks at the current at the base, and adjusts the current at the collector so as to be a multiple of the base current.
It is the transistor's ability to amplify a small control signal to provide a larger output current or voltage that makes it so useful.