Let's take on that controversial issue. Okay, there is some truth to those statements, in some contexts. This is totally irrelevant to the world of guitar distortion. The holy grail of guitar overdrive is thought by many to be the distortion that goes on in a tube power amp. All the classic guitar amps have push-pull output stages which, due to their symmetry, only generate odd harmonics.
Transformers also tend to create odd harmonics when overdriven.
Crank those amps all the way up, and they produce even and plenty of odd harmonics, and we love them for it. Just don't play your Esquival records through one. The fact is that both even and odd harmonics are important to getting a good guitar sound, and both can be generated with either tubes or transistors. We were going to keep this about phenomena, not technologies. Most of what makes an overdriven component sound the way it does, then, is how it shapes the corners that it adds to the wave, and whether it treats the bottom and top half the same way.