My personal rule, if I'm the shooter and the hit will be close, I'll ask my opponent if they want to have someone watch the hit/shot.
Usually the first time I play someone (during regular season), I try to assess their honesty as well. I would expect my opponent to do the same (as above) when it comes to close hits.
The key is addressing the potential problem before it happens. How many times has your opponent dashed to the other side of the table to shoot the ball before you even say anything ?
My go to line (and you always have to be watching the game), "Depending on what you shoot, I may want someone to watch the hit".
In lieu of a neutral observer, if the hit is close and/or questionable, I look to my opponent to make the correct call. In close cases, where I myself can't be 100%, I'll defer to my opponent. If he/she picks up the cueball and/or says, "Ball In hand", no harm no foul (barring that obvious pun).
All that said, the first time I see an obvious foul (when he/she and I KNOW my ball was hit first), and my opponent doesn't call it, from that point forward anything that might be close gets an extra set of eyes.
Recent case in point: A player in my league (Paul) is notorious for these kind of hits as well as push shots and double hits. In my own games as well as other players.
"Split hit goes to the shooter" is his go-to when anyone questions the shot afterwards.
So I'm playing Paul a couple weeks ago. Where his cue ball ends up, my ball is roughly 30% in the way of his. He has two other good shots, but no easy way to get back to the shot with my ball in the way.
If he shoots that shot, for his ball to drop, he would have to hit my ball first and follow the cue ball...
Me: "Depending on what you shoot, I might want someone to watch the hit."
Paul: "Hmph... Ten in the corner."
Me: "Ok, lemme grab Tim (my captain) or Will (his)"
Paul: "What, it's not close."
Me: "Close enough for there to be a question."
Paul: "Split hit goes to the shooter."
Me: "I know, and we'll get someone to watch the hit."
Paul: "What, you don't trust me ?"