The thing to note is that (good) tube amplifiers can be designed to be very linear until they're driven too hard - the audiophile community often overlooks this detail when they're shopping for "warm" tube amps for general power amp duties. The big differences between tubes and other kinds of amplifiers appear when they're driven at, and especially past, their design limits.

In an application like a guitar amplifier, some kind of effect/distortion pedal, etc the tube circuit is typically overdriven by design to get all of those warm harmonics. A tube that isn't being overdriven is every bit as capable of being a "wire with gain" as any kind of transistor or more modern circuit.