Your link does not support your claim, exactly. And while it may be the case that there is pain from the process of passing the irregularly shaped (and often sharply pointed in places) object, the vast majority of the pain is located in the renal area regardless of where the stone is blocked, and caused in large part by either the damage done by the stone upon exiting, or the backup of the flow of urine in the kidneys.
I’ve passed 10 stones. The last stone managed to get lodged in the ureter somewhere between the kidney and the bladder, quite low down (they weren’t able to use lithotripsy it was so low down). It stayed there, causing intermittent symptoms for several months, before finally acting up for good over the course of several days, forcing the urologist to take his laser to it. In each case of symptoms, the symptoms were located primarily in the location of the affected kidney; some mild, secondary discomfort at the site of the stone rarely was sufficient to do much more than have me take an ibuprofen. For those who don’t know: ibuprofen doesn’t do diddly with kidney stone renal colic.