I thought "rendre visite" was used for people whereas "visiter" was used for places. Or is this different because it is not a specific person?
You're absolutely right. I actually posted a comment already a few weeks ago on this subject, but apparently, the sentence has not been changed since.
could this not be elle visit un person malad? i.e. for visiting a sick man?
No, it can't. "une personne" is always feminine, whether or not you are talking about a man or a woman.
is 'elles visitent...' not also correct?
Yes, because there is no difference in oral here.
However, a liaison should be made between "visitent" and "elles" VISITEU-T-EL
I made the same mistake ... i.e. using the plural - even slowed it down just to be sure