I believe Nayru had just a perfect amount of trial to recieve the song of the hero.
However, i think the Water Dragon was highly too skeptical, considering we already had her scale, she'd already lent us the basin after we completed an entire dungeon under her awareness, and we had brought her sacred water. Also, she had given us direction into which the Sacred Flame was. She obviously knew we were the hero, and we shouldn't have had to prove it again, when she clearly was aware of who we were.
Whereas, the Fire Dragon was very easily trusting. If he hadn't erupted the volcano and we wouldn't had to do the Bokoblin Base, would he still have believed we were the hero, just by having earrings that protect us from fire? I felt nintendo should've played up his skepticity or something that showed they were all doing their job's correctly, and wouldn't teach the song of the hero portion to any random person who could walk up a mountain.