Paul argued this at length in his Posts when he brought out the pre-amp. If it changes the sound for the better, then great. Consumer audio is only a trick, so there is no real objective sonic truth. You only have to go to a live acoustic or vocal performance to realise that. So having read loads of Paul’s posts, he’s convinced me that coloration is a good thing because if it makes people happy and the music sounds more realistic to them, then the trick is working better and money has been well spent.
What cannot be correct is the idea that a pre-amp can add anything to the incoming signal.
It’s more a matter of what you think a pre-amp is. I’ve always thought of it as a switch box with attenuation. The only one I ever owned was totally passive, no power on the signal path, and the only components on the signal path were a couple of resistors. A gain stage is like any other amplifier potentially going to colour the sound.
If the BHK pre-amp is “improving” the sound, what is it doing and was that the plan when it was designed? That would be an objective assessment.
If a user just likes what it does, then great. For my part, I’ve always been happy with one stage of amplification and see no point in adding another for no good reason.