playing someone or indeed having someone at work whose mind is elsewhere can not only mean their mind isn't focussed to do the job right so they can be a hinderance/have a negative impact on certain outcomes (through no fault of their own) but also potentially be a danger to themselves and others.
saying no is not an option in these circumstances, not only do you alienate the individual and there's a high likelihood they'll just go/not turn up anyway, you cause yourself no end of grief with employees/colleagues and potentially local community even business partners/investors etc.
mind you when someone comes to you and says their 'gran' has died... for the third time in 5 years (a real gran, a step gran and a gran in law is all i could imagine a senario for) some people do take things a bit too far at times.