Swiftech quotes the article because peeps are running THEIR PWM PUMPS off variable voltage signals... not the other way around. They don't have DC voltage controlled pumps so if what you are saying was correct, there's be no reason for Swiftech to issue this warning.
Pulse-width modulation of DC operating voltage to modify fan speed [edit: in PWM devices] is not recommended. Transients generated by that approach can irreversibly damage motor commutation and control electronics and dramatically shorten the life of a fan.
What they are talking about is the "so called" PWM fan controller that are not modulating speed PWM but by variable voltage.
"Pulse-width modulation of DC operating voltage" - What they are saying is that the fan controller is converting a PWM signal from the MoBO and modulating DC voltage accordingly ....
This is the same thing you can do with a 4 pin header. I will note that a 4 pin header is not necessarily PWM. Most Z87 boards have 4 pin chassis headers which do not provide PWM control, but rather DCV control. In Z97 , for the most part, they may operate either way. So a 4 pin header can control via DCV... this is a bad thing for PWM devices. As the OP clearly states, "the 3-pin header provides a variable voltage." That's exactly what Swiftech is warning about .... PWM devices want 12 volts...not 7. not 5, not 3..
"[using] DC operating voltage to modify fan speed [edit: in PWM devices] is not recommended" - Again, clearly, the speed of the item being speed controlled is a PWM device.... not a DVC device. And using variable voltage to control PWM is not recommended.
If that is not clear enough
What is important to understand above is that PWM fans, and the Swiftech PWM pump, are designed to receive a fixed 12 v supply. While the voltage may vary somewhat, the range is usually limited; we’ll publish the safe operating range for our pump upon release.
The OP clearly stated that "the 3-pin header provides a variable voltage".... exactly what Swiftech warns against. PWM fans and pumps, are designed to receive 12 volts so as not to experience the problems listed.
And again:
This controller may use the motherboard PWM signal to manage the fans, but it still manages them thru voltage modulation, therefore this would not work for our [PWM] pump [or PWM fan].
You do not want to use voltage modulation to control PWM which is exactly what Swiftech and Nidec are saying.
As for the advantages of PWM, the information is somewhat outdated and that's the very reason Swiftech has this warning. Well not outdated so much as it leaves out the "hybrid" category. The PWM controllers they are talking about all advertise PWM control because that is generally considered superior. And they do use the MoBo's PWM signal to control speeds.
They, like the Phanteks fan PCB use a PWM signal to output a DC voltage. This provides a "best of both worlds" approach. You get all the fine and low speed control w/o the low speed problem. These devices get fan speeds down to 20-25% an area not usually possible with DC direct voltage control. You also eliminate the low speed clicking or hum of PWM fans. In the end now we get PWM control using 3 pin fans that cost 1/3 to 1/2 as much, w/o the hum / clickety noise and we still get low speed operation, even ramp them up and down as well as turn them off and use passive cooling at low loads.
But as Swiftech and Nidec state this quite clearly. PWM is designed for 12volt operation and not for variable voltage operation. If it was the "reverse situation" as you suggest, Swiftech wouldn't have a full page dedicated to eliminating the misuse of their PWM devices devices.