Yes, I've had a few of these in my time (as an HR manager). The general approach I took was 'if you are sick enough not to be able to work, then how can you possibly feel well enough to travel - shouldn't you at home getting better and not infecting others'.
It does, in my opinion, rather depend on what the problem is with the person, and more importantly, what the person's previous attiturde to sickness and absence has been. Being told that holiday is good for health doesn't carry any weight with me.