It’s seems very odd to me to go to your boss with evidence of the closeness of your friendship with the deceased to demonstrate that your closeness of relationship warrants that being entitled to an extra day’s leave. You’re effectively saying “Look at these photos and documents that show how close I was to this person... Surely you now feel sorry enough for me that you’ll give me an extra day’s leave.
Well nobody is asking you to
But if you CHOSE to argue that this is the death of someone you have a close but non blood relationship with, more than just a regular friend. Then it makes sense to describe it as such!
If you "just" ask for leave for a friends funeral. You'll just get annual or unpaid leave
It's your choice. Nobody will make you describe or give details of the rekationship, but if you leave it at that you cannot seriously expect your employer to assume I'd psychically know that you are closer to this friend than your own blood!
What I am saying is that if you are really as close to a friend as the OP is arguing some people are to friends, then you will either have some other more accurate way to describe them (best man, birth partner etc), or, you will have some evidence to hand to show it as more than "just" a mate.
I found it easier to just snap a photo of some certs and attach it to an email than to argue my case when devastated. And it worked, I got the CL.