Honestly, I've seen a lot of people put a lot of thought into it just because of the little red diamond. I'm not going to disprove the theory but instead this time around i'm going to try and say why it could be, or, what I believe, couldn't be.
First, for saying why it could be:
1. Fi and Ghirahim both call their "wielders" master. While this may seem like a stretch, it can make sense seeing as Fi always calls Link master and Ghirahim does the same for his own.
2. Secondly, If we look at the sword it's not really black but is dark and red, as is Ghirahim's cape. If we look at Fi's shawl and Ghirahim's cape in the same way, it could make sense.
3. As for the diamond pattern that is found on Ghirahim? Take a look at the jagged edges of the sword itself. They jut out and in like fused diamonds.
4. Of course there's the infamous diamond that a lot of people have been speculating on. It's not a very strong argument, seeing as how it's a recurring theme used by many in the game, but it's still a small one.
Reasons against why Ghirahim is the sword:
1. Ghirahim was depicted in the battle in the intro and it would be odd to have him as a fighting demon there and a wielded sword now. Though if he was turned into one because his master was ticked at him remains to be seen, it's still a stretch.
2. Ghirahim has powerful magic himself and also wields a sword. A sword wielding a sword? It's not likely.
3. Fi is more spirit like in her form while Ghirahim seems to be much more physical, like an actual human being.
4. A sword would not likely have a title like Demon Lord Ghirahim, and seeing as he is advent on being called such, it's a large stretch to call the sword that.
5. The upside down Triforce... We know why the Triforce is on the Master Sword seeing as we have to imbue it with the power of the goddesses who made Hyrule. It doesn't make sense why it would be upside down on Ghirahim as a sword when he wouldn't have gotten the power of them. (unless the goddesses had one really sick sense of humor in the beginning of time, but unlikely.)
Another theory that I came up with while typing this all out is the Triforce... Perhaps the master obtains the Triforce and wishes for a supremely evil weapon able to counter the Master Sword. (Why he wouldn't just wish for death and destruction is beyond me... self satisfaction?... I digress again.) This could account for the upside down Triforce on the blade since it would be an ugly, evil, corrupted version of a Holy Weapon and the symbol would/could reflect this mockery.