Clear a phone for use

For information about how to request access to a deceased family member's Apple accounts, and through this their equipment, click here --> How to request access to a deceased family member's Apple account - Apple Support

Apple does specifically mention a court order.

Sorry for you loss.

As explained in the support document you posted from, you need to get a court order if you are in the U.S. In other countries other legal documents such as a power of attorney may be enough. In the U.S. a court order is required.

You can contact Apple Support directly for more help and guidance by clicking here ➜ contact Apple Support