Tri-amping gets complicated and very expensive.
As a 3-way Maggie owner, who has converted his Maggies to 3-way active, I'd have to say that the above statement is one of those oft-quoted, supposed "home truths" which have a skerrick of gold surrounded by a slagheap of dross!

I guess the order of "complicated" might go something like this (from simplest through more complex):
* integrated amp and single-driver speakers
* integrated amp and passive, multi-driver speakers
* preamp and active, multi-driver speakers (with in-built power amps - like ATC)
* preamp, power amp and single driver speakers
* preamp, power amp and passive, multi-driver speakers
* preamp, stereo power amps and active, multi-driver speakers
* preamp, monoblock power amps and active, multi-driver speakers
* etc.
So, yes, there are more components to plug together in an active setup (except when you have ATCs) but is it really more "complicated"??

And re. "expensive" ... yes, in a 3-way active setup you have to buy 3 stereo power amps but these could be (rated into 8 watts), say:
* 100wpc for the woofer
* 60wpc for the mid-range, and
* 25wpc for the tweeter.
The "rule of thumb" for comparing watts in an active vs. passive setup is that a single amp has to have twice the sum of the ratings of the two amps used in the active setup, to deliver equivalent power ... so for a 3-way active setup, you'd have to have a single stereo amp capable of delivering 370wpc for equivalent passive power to the above active system.
I suggest to get a "big" amp which sounds as good as the 3 smaller amps might, could in fact cost more than the 3 small, cheap amps.
Regards,
Andy