In the world of guitar amps, there's a sliding scale at work. The cleaner you go, the greater the role of the guitar, and the dirtier you go, the greater the role of the amp. There isn't a fixed break point, instead there's a continuum in which the guitar predominates at first, and then the amp takes over as distortion increases.
In other words, arguing about which is more important, amp or guitar, is to aim at a moving target.
One needs to qualify whether you're talking clean or dirty, and where on the spectrum between clean and dirty you're listening. And because different pickups drive amps differently, even similar guitars with different pickups will sound different.
The guitar is crucial because it's your base tone. But that's just for starters.
The amp is crucial even clean, because it colors whatever guitar is run through it, so it more or less has the 'last word' on the tone. Even so called 'clean' amps typically have more than 10% distortion, and the distortion runs much higher when the gain is increased. If you've never run a guitar direct into a recording rig or hi fi amp, you've never heard a truly clean guitar tone. To me, a direct signal without an amp sounds pretty awful (but George Harrison and some of the funk players might disagree).
At very high gain, much of the guitar's tone is obscured by the amp clipping - this turns the sine waves into square waves. Square waves eliminate true high end, exaggerate low end, but a clipped tube also generates its own harmonics. These harmonics give you high frequencies, but that's mainly amp, not so much guitar.
A fuzz box is a square wave generator, and so is a very highly distorted tube amp. I'd bet it would be difficult for anyone to identify exactly which guitar is used on a recording to generate the signal for a fuzz box without knowing in advance.
Thus the amp tone takes over completely at some point on the distortion continuum, which is why (for example) people thought Page's guitar in the first Led Zeppelin album was a Les Paul, when in fact it was a Telecaster. It's very difficult to identify what model of guitar is making an extremely dirty sound.
Played clean, I agree that the guitar rules. Played dirty, I think the amp rules.
Everyone gets to be right!!