I think a company need to balance work life and personal life, as you said he has worked for 4 years now and have taken 0.5 days leaves per month due to sick or some other reason, this shows that he is a responsible person, he worked for half day when he was sick.
Now that he need leave for his crucial situation happening at home we should support him. these are the situations when company can build its long term relationship with an employee. Knowing that he is handling a most responsible role in company, but apart from it he is also a family man.
I will share my experience in my last company, I was a HR Manager and after a year I had to take maternity leave for 3 months and also took extension of 2 more months, after that when I rejoined I had also asked for a request to work on half days for a month, thereafter I had also got adjustable working hours, instead of reporting office at 9 am, I got authority to report at 11 am and can leave once I complete my responsibility for a day. I would also manage calls from home.
I am really greatful that I have worked with a company who was so much supportive, this is how I spread my message to everyone about the goodwill of a company.
I think you should help him and ask the valid documents for the leaves, if you are satisfied with the documents provided, discuss with your MD and go ahead for granting a leave, he will be greatful about the company.
Regards,
Sanjukta