Well the bladder is a sphincter too, and once in a while especially when you become older it doesn't hold it's own like it always should. therefore it makes sense that the anus and rectum can undergo premature loss of function if exposed to too much wear and tear...
hehheheeh... For interest sake go look up some images of ANAL PROLAPSE on google
Actually the bladder itself isn't a sphincter. It is a muscular sack that stores urine. It does however have two sphincters that control the release of urine. The first is internal and involuntary and the external one is voluntary and you control it.
People become incontinent due to an inability to control the second one and this could be due to a problem with the sphincter or a problem with the pudendal nerve, which controls it.
Not all old people become incontinent, just as not all people who practice anal sex get prolapsed rectums (This is called an a** tulip in pron by the way, check out Audrey Hollander, its her speciality). It is a one out of a hundred or more thing (I suck at stats). Proper care prevents it from happening, if done right.
The a** also has two sphincters, which is why its sometimes possible to get in a little bit, but then it hurts when you go further. Then you have to let her relax and add some lube before the second sphincter relaxes enough to make way.
You're a med student right? I don't think you're lecturers would be too impressed with you referring to the bladder as a sphincter.