Can a PWM fan be turned on and off through the control pin? Or can it only adjust speed? Is it just a fet that turns the 12V on and off?
Before 4-pin fans became common, people had to build their own fan controllers to change the voltage applied to 3-pin fans. Some folks used rheostats, just burning off the excess power as heat, others chopped the incoming 12V, making a rudimentary form of buck converter.
The 4-pin fans simply integrated the PWM control circuit inside the fan -- this may be implemented in many ways, all dependent on the fan model. Dead simple brushed DC motors probably have a single FET in there that is roughly chopping the voltage. If there's a fan built with a BLDC motor, it's probably using the PWM signal to drive the BLDC motor controller.
Your fan's datasheet seems to show that at PWMs below roughly 10%, it will not spin (for a 12V supply). If it is actually spinning, I would measure the voltage on the PWM line -- perhaps something else is driving onto it.