I'm sorry to hear of your loss.
Lots of other people have mentioned legal, professional, other issues, et cetera, but my answer to your question would be this: No, your supervisor is not correct: They are acting inappropriately.
Think of this as a matter of priorities:
During your professional life, you will work for a few organisations. Many of them will be quite realistic, as far as your current exercise is concerned, and you will frequently encounter situations where your supervisor will run a team ragged, and insist that you make up for the lack of budget (or prior planning) by sacrificing your personal time to compensate.
Should the amount of time you spend on their project lead to burn-out, or even a divorce, they will not care - and will simply chew you up and spit you out, the moment you've outlived your usefulness.
Your family, on the other hand, is not just a higher priority, but in a category of priority that no employer could (or should) ever hold a candle to. They are with you for life, while an employer is only with you for as long as you are more valuable to them than the amount of money they can get you to accept.
By all means, be professional and inform your employer that you will be attending to your relative, rather than forcing them to wonder what happened to you. However, to use the RACI model in ITIL, your employer moves from the Consulted category to the Informed category, when it comes to urgent family matters.
By the way, enjoy the funeral. It might sound like a strange thing to say, but it will be one of those few events in life that really pull your family together. The last funeral I attended made me realise just how important and precious the whole family was, and how much we missed seeing them all together.