The only Medallions that are required to get the Light Arrows are the Shadow and Spirit Medallions. The reason for this seems to be that the developers assumed that the Shadow Temple could not be reached without obtaining the Forest, Fire and Water Medallions. So instead of testing if all 6 Medallions have been obtained each time you enter the Temple of Time, the game only tests for the Shadow and Spirit Medallions. With various techniques, it's now possible to enter the Shadow Temple early, allowing you to skip the first 3 Temples. The Spirit Temple is required because it can be completed at any time, even under normal circumstances.