I know what you mean (I think), but I would put it differently:
Faster transients should mean a less bright sound. I.e. that the transient is handled exactly right, without overshoot, overhang or ringing. When a component appears to put emphasis on transients, i.e. appears brighter, it is probably due to some combination of overshoot, overhang or ringing.
I have no idea where the 009 fits into this, but I don't think the BHSE has a problem in this area - at least not with the right tubes ;-)