Adriaan,
I don't disagree with you. Playing a lot of covers, I find that a relatively accurate representation of the original tone often works better than a 'perfect' bass tone. For that, I have the Bass Pod XT.
My favorite pure tones come from things like the Mesa 400+ or the Alembic preamp, though I currently own neither. I've got one of the original Baby Blue amps that does pretty well. I like to think that I can be as much a purist as the next guy when the situation calls for it, but I consider myself fortunate that it is not an obsession for me. On the other hand, I generally won't buy a bass unless it sings to me acoustically. I firmly believe that you have to start with good wood to get great tone.
When I refer to flat, I meant more that I didn't tweak a lot of knobs during or between tunes to alter tones. This habit goes back to the old active basses I had in my youth where trying to alter the tone from the bass would add significant noise. I am not old enough that I couldn't have had an Alembic back then, but that was not my lot.