I can definitely see what some of the previous posters have stated....essentially, the assumption had always been that the shield design had been inspired by the royal crest. However, it's very possible that the shield was what actually inspired the royal crest.
Although, another explanation is that they are entirely independent of one another and both coincide with a monumental event in the game. I could imagine a scene late in the game where Phi, or the goddesses, or something; finally disclose to Link (and possibly Zelda at the same moment) the truth of the Triforce and its location. Based on our limited knowledge of the game, it seems like the people of Skyloft are slightly ignorant to the creation story and the Triforce (simply based on the fact that the Triforce imagery is missing, there is a single "goddess" statue, and there is dialogue discussing a "goddess" and not goddesses).
So maybe there is a single, shared moment where the royal crest/shield imagery is actually given to Link & Zelda to show the connection between the people and the goddesses...a sign of a "contract" to some extent, and a visualization of the power/importance that the Triforce holds over them.