Effect of emitter capacitor in common-emitter amplifier
Your reasoning is correct.  As pointed out in the comment, approximations are very useful in reducing the amount of calculations required to determine the performance of a circuit.  In general, most transistor circuits are designed to make their performance independent of transistor parameters as much as possible because those parameters are quite variable in practical transistors.  In this case, a good approximation, as you already know, is that the value of the emitter resistance is much smaller than the external resistor.  This greatly simplifies the calculations.  In any case, tolerances on components will probably swamp out the value of the exact calculation.