Who said he was aiming for the head. Maybe he was aiming for the chest and the bullet sailed higher than he intended.
Good point. I thought about this, and it was only after I'd gone to bed that the ideas gelled. While a gunshot to the head is Movie dramatic, a miss is more Literary dramatic, as it stretches the action out, allowing more reactions shots.
Imagine this: while speaking (you'll need to include part of the speech) the speaker starts waving his arms, turning to encourage the crowd to participate, when he's suddenly thrown back. Everyone just freezes in place, dumbstruck, and then the gunshot reaches them, causing everyone to duck and glance around, trying to figure out where the danger is.
At this point, your character can start reasuring people: "The shot came from the northwest, and he's not firing randomly, this is a trained sniper." That clearly identifies him as an expect, and the 'go to person' for the rest of the crisis.
But the best part of a miss, is the shooter will then need to fire again, at which point the panic sets in, and people start running everywhere, making it difficult to respond. At that point your MC starts issuing orders, telling people the best places to hide and where not to run. As they begin to listen, he finally can run to help.
Since the speaker would have been knocked down, he'd presumably be a harder target, possibly shielded by various objects, so the shooter would then have to fire shot after shot. And with each shot, more people panic and bolt, furthering the confusion.
That also makes rendering ... problematic when they're an active shooter firing at you. Any nearby bodyguards or police, when encountering the MC can shorting your background. "Your a vet?" "Yeah, Afghanistan, two tours." "Well, we'll glad to have your expertise. Now what should we do?"
They then struggle to drag him to safety before he's killed, ramping up the tension. If one of the rescuers ends up getting hurt, or killed, it reinforces the tension, as well as raising the stakes in the investigation, as it goes from a simple assassination attempt to a 'Mass Shooting', meaning EVERYONE in the city will want to track down the shooter, and his 'rescue' gives him credibility with the authorities.
Best of all, if the intended target IS killed, it doesn't take anything away from the story. The MC can perform emergency treatment, trying to save him while still under fire (since the EMTs aren't likely to brave open gunfire). As he's performing aid, he can shout instructions to any nearby cops, since they're unlikely prepared for active sniper events, which sets up the search for the shooter, which takes place while the MC is still being debriefed (and obviously they don't find him, despite he's presence being compromised by his taking repeated shots).
By stretching the scene out like that, you can bring in a range of new characters (people who helped, people who volunteered, people who hid and then pretended to be brave afterwards, and those who provided idiotic advice who helped no one), establish the MC's bona fides with short-answer background information, and give him semi-automatic credibility. Throw in a pithy death-bed confession by the victim, which the MC is tasked with delivering to his family, and you've got emotional drama dripping all over your pages! That's much more effective than a simple 'one shot and done' gore scene. Imagine him being interviewed back at police headquarters, still wiping the blood off his hands as they're bringing him coffee and thanking him for saving their fellow servicemen.