Diverticulitis affects the upper intestines so anal sex wouldn't affect the diverticuli in any fashion. If, however, she is suffering from frequent bouts of diarrhea then she might want to consider taking a fiber supplement and wait until she has cleared it up to try anal sex without a condom. We find that deposits left during a bout can cause burning of the penis...gross I know but still...
The worse thing you can do when the diverticuli are inflammed is eat complex hard to digest foods so a bland diet is recommended until you are free of pain and then slowly bulking up the stools so that the colon is uniformly full and evenly working.
Ignoring the problem can lead to necrosis of the colon and possible surgery to remove the dead tissue so if you have pain under the ribs, frequent constipation or diarrhea, accompanied with fever then see a doctor.

An interesting thing to note is the susceptibility of developing diverticuli is probably genetic and more prevalent in women....possibly related to hormones. Western and European women tend to develop the diverticuli on one side wheile Asian women tend to develop them on the other side!

Either way it is safe to have anal sex if you have diverticuli or have had diverticulitis.