The tube itself doesn't have a characteristic sound. It's just part of the whole system. Tubes with different parameters will impart a different sound, but the circuitry of the amp itself is the other half of the total equation.
It's the sum of the parts. No single part has the sound.
From a FUNCTIONAL perspective, yes, you can swap tubes and get a variation in sound. Nobody has said otherwise. But the tube is just part of the sound, as is the tone circuit, as is the output transformer, as is the speaker cabinet and the speakers within it.
I would introduce you to the concept of the "transfer function" as applied to electronics. The transfer function is the response modification of the input signal. How the input signal is changed by interaction with a specific device. Even a single wire has a transfer function. So does every tube, every transistor, every capacitor, every resistor, and every transformer. Your entire guitar signal chain has an aggregate transfer function. Every part of the chain has its own transfer functions. It's the TOTAL transfer function that determines the final sound. No single component is responsible for most of the sound characteristics.
A given tube that may make ONE amp sound brighter than with a given reference tube COULD make another amp sound warmer, depending how the circuitry of the two amps are different.