The NCDOT Raleigh-Charlotte trains are dispatched by NS, and things run just fine. It's true that the underlying railroad is owned by NCDOT, but that doesn't matter much in day-to-day operations. The contract between NCDOT/NCRR and NS clearly gives NS dispatching rights.
Everyone knows who's in charge. If NS started delaying passenger trains for freights, they wouldn't get their contract renewed.
The question, really, is whether the track in question has sufficient capacity for both passenger and freight, relative to the number of trains that traverse it. If the track does, a dispatcher won't have to make difficult decisions very often. But if the track doesn't, it really doesn't matter who dispatches it -- there will be delays regardless.
To freight trains, yes.
People seem to think that dispatchers are either the devil incarnate or omnipotent. The truth is, neither.
You make it seem much too simple and act as if it is out of the control of the dispatchers -- which isn't true at all. The difference between hostile-to-passengers dispatching and friendly-to-passengers dispatching is actually quite blatant and obvious most of the time. Though in some cases I've also seen what looks like simply sloppy dispatching (not paying attention).
Of course, it's possible to give a dispatcher an impossible problem ("Here, we've assembled a million very long extra trains for you to put through a single track line, and we need to shut the line down for maintenance.")
But consider the case where the dispatcher is faced with a somewhat crowded double-track (or largely double-track) line where the dispatcher can choose to give passenger trains priority or not... it can be pretty darn clear when they are doing so and when they've been instructed not to. Little things like whether you're passing freight trains going in the same direction, or whether they're being run ahead of you.
I've been on some really impressive passes on BNSF track, with one freight train in the right-hand siding, another freight train in front of us, passing onto the left track to pass that train, and then back onto the right track, with another freight train waiting to go the other way. BNSF has also gone out of its way to provide detour routes when there are problems on the track. I've seen some fairly heroic dispatching from Norfolk Southern as well.
By way of contrast, on CSX in NY, they don't seem to even try to pass passenger trains ahead of freight trains, but I've seen them pass freights around stopped passenger trains. Some of this may have to do with the numerous one-platform stations requiring specific track allocations, but still, the difference in attitude is noticeable. CP seems to have an even less friendly attitude towards passenger trains. And Amtrak has documented CN's behavior in detail in STB filings.