Ah, ok, got it now. I was discounting the woofer response too much, incorrectly.Brightness is the result of a bump in the upper mids/lower treble. Any tweeter will emit this freqency range very wide without additional means to prevent it (wave guide, horn, ...). Woofers on the other hand beam in this range, whlch here leads to the directivity error.
Thanks for your patient responses.
I'd be interested to see a proper spin of this speaker, showing also the summed response/expected in-room. We don't see that here.
I wonder if it's worth trying to do some measurements at the listening position -- I've been meaning to do this. WIll only apply to my room and have all the usual problems of not using a proper rig or anechoic chamber, but I've been meaning to do it anyway.