Here's how I read this (and confirmed by opening iTunes, doing Store > View Account > Manage Devices from the iTunes menu):
This note comes from the article you attached. The underlining is mine (for emphasis):
Note: Removing a device from your Apple ID does not override the 90 day timer. The timer must complete 90 days from the day the device was associated before it can be associated to another Apple ID.
So from the time you originally associated the device (around the time you registered your device) with your Apple ID, at least 90 days must elapse before the device can be associated with a different Apple ID.