How should I put it? Sherlock had not actually lied to Hawkeye about any of this, though it was not exactly the truth either.
At first, Sherlock had wanted to create the kind of magic arrows seen in movies—arrows that could summon wind and rain while flying toward their targets, or produce all sorts of magical effects after striking them.
But Sherlock later discovered that achieving that was simply too difficult. Even combining it with Asgardian technology had not been enough, so he had settled for this current "Wish-Fulfilling" version instead.
The reason "Wish-Fulfilling" was in quotation marks was simple: true wish fulfillment was even harder to achieve than magical arrows!
So this so-called wish fulfillment was actually much like making a wish at Yonghe Temple.
To give a simple example, suppose Hawkeye fired an arrow at Chitauri Soldier A while wishing it were an explosive arrow. There was a good chance the arrow would not hit Chitauri Soldier A at all.
Instead, Chitauri Soldier B riding a flying vehicle might suddenly appear in its path. The arrow would hit Chitauri Soldier B, causing the vehicle he controlled to veer off course, crash into Chitauri Soldier A, and explode beside him.
Of course, that was only the ideal scenario. After all, who could guarantee that they would not be the so-called "Chitauri Soldier B" at that moment?
To put it plainly, the Elven King's Wish-Fulfilling Quiver was just like Yonghe Temple. Never mind how the wish was fulfilled—just ask whether it had been fulfilled or not.
Of course, aside from that somewhat unreliable "Wish-Fulfilling" feature, there was another benefit. The moment Hawkeye equipped the quiver, he went from a somewhat handsome middle-aged man to a stunning long-eared elf who looked beautiful enough to glow.
His face was still the same