I had always figured there were about five alternate realities where that was the case. One for the deku scrub, and four more for each dungeon explored. The only part I disagree with is the part where Link is crushed by the moon, since playing the Ocarina of time would pull him into this newly created timeline, taking what few items it could with you as you go.
I don't really know. I've found that there are plenty of bad theories out there that simply ignore canon. . . such as Link being Dead in Majora's Mask. I didn't agree with this theory at all because it would mean that Link couldn't have become old enough to get married, or have a child who would later spawn the Link we know in Twlight Princess. I do believe that Link became a skeleton spirit and "Hero's Shade" as we see in Twilight Princess however. I had always theorized that the single red eye in his skull was some kind of a moon pearl as seen in A Link To the Past, which allowed him to transform into a golden wolf at will, although I know- that's a pretty far stretch.
I think that the best theory I've looked at has to do with the Twili, Majora, and the Fused Shadow connections. The only hard part is figuring out how people from Termina could be connected to an entire race that was banished long ago since not too many people in either realm seem aware of another's existence. But it is possible, and I would say that the Fused Shadows most definitely have something to do with the original Sheikah, and the Shadow Temple in particular. For a children's game, it got quite deep and dark at times.
I have thought about this a lot myself. I never played the Oracle games, but for me, it seemed that the fourth piece was most likely for the Goddess of time as mentioned in Major's Mask. I never believed that it was truly canon, but I did wonder if this fourth piece became the Ocarina of Time itself, only under disguise by some strange series of events. Curiously, the Ocarina of Time's greatest power seems to come forth in Termina, where the Goddess of time is mentioned and revered the most.
I had a theory that when the Three Goddesses created Termina by accident. . . they had not only made several strange copies of places and things that existed in Hyrule- but also people which were doomed to mirror Hyrule's inhabitants for centuries. The Feirce Deity may have been some mirror image of the First Link mentioned in Skyward Sword. . . The Goddess of Time, I came to believe must have been some parallel to the Goddess Hylia who was also mentioned in the same game.
I realize that there is a lot of conjecture here, but. . . It's still neat to think about. OOT and MM are the two Zelda games I have played the most. I also played them when I was young enough to really enjoy them, but also understand some of the deeper themes portrayed within both games.
If I had to guess, I would say there was some connection between the Goddess of Time. . . Hylia, the Ocarina of Time and other elements in Termina that would comply with this "fourth piece"- If it were to be canon. And I'm pretty sure it's not, but I still support the idea. If that's alright to support an idea that probably won't ever be used by the Zelda Staff.
We know the original inhabitants of Ikana certainly thought. . . something of Tri force. I am disappointed that MM3D removed all that. It had so much lore going for it. . . especially with the sacred light arrows and all which the Ikanites apparently had kept for ages inside the Stone Tower.