it does indeed seem like cynical oversimplification.
I havent tried the PD7 in years but I've used the TS9b a few times.
From what I cant tell, the mix control on the TS9 b doesnt actually blend in the clean tones, because its still overdriven no matter where I have it set. There is a slight mid boost from what I can hear (like a regular tubescreamer) and the EQ is pretty rad.
The PD7 can get very sizzly and clanky using the 'attack' controls from what I remember and doesnt seem anywhere near as well built (however considering the price difference, its not really a factor).
In all honesty they seem totally different, the PD7 boosts the harmonics and scoop the mids - kinda like a metal-playing guitarists idea of a bass distortion.
PD7
‪Ibanez PD7 Phat-Hed Bass Overdrive Demonstration‬‏ - YouTube - this is how I remember it
Bass Tubescreamer
‪TS9B -Bass Tubescreamer-‬‏ - YouTube - pretty close to what it actually sounds like to me.