Butterfly Mage is pretty much right-on with his assessment!
I work daily in a detention center in a north-eastern county of Maryland, and he's pretty much right on the spot according to what I've seen. Incontinence is a rarely-experienced ailment, but it's still a potentially embarassing and unhealthy ailment nonetheless, which means that fellow inmates would be at the risk of being exposed to urine or fecal matter, which also carry any other volatile diseases. Somebody medically proven to suffer from incontinence would likely spend their time in medical isolation to ensure their own medical safety and privacy, their social safety (because fellow inmates won't likely be so forgiving), and the medical safety of their fellow inmates. I know that this is the case for inmates who are elderly, as well -- their frailty suggests that they remain in a separate area to keep them from experiencing any unfavorable interactions with fellow inmates.
I'm of a mind to believe that this whole idea of people in jail being given diapers is just glorified fiction. Inmates aren't allowed to have anything but specific kinds of clothing, and the material on absorbent undergarments could potentially be used for any number of undesirable actions in jail (including, but not limited to, harming other inmates by suffocation, hiding disallowed objects, or bearing chemicals or a mixture of chemicals) potentially harmful to other inmates). If they get diapers, I imagine it would be in medical isolation. Otherwise, what you hear (or even see) are probably just rumors or special circumstances, to my knowledge.
I know that in the case of anybody who's just too lazy to use the bathroom except in their own clothing, they're responsible for cleaning it up and taking care of it. They won't promote someone being lazy and answer to their every beck-and-call. There needs to be medical documentation that approves the presence of incontinence before any other action is taken.