The problem, as it relates to gunfighting, is that raw marksmanship is only the most basic foundation (you can't possibly hit under stress, unless it's luck, if you can't hit under no stress-demonstrating you have the hand-eye coordination to place a bullet). At the fundamental level, yes; hitting a small target far away is the same skill as hitting a target closer and faster. Trigger press w/o disturbing the gun, sight alignment (or body alignment), some sort of time constraint, some sort of acceptable group size.
That is apples to apples, range-target marksmanship. The problem is that hit rates in gunfights bear little to no correlation to the range. The same person who as an example can shoot an 8" group at 25 yds then only hits an entire person 1 out of 3 times in a 3yd gunfight. The answer is not to work with them until they can shoot a 4" group at 25 yds, improving their poor marksmanship. Heck, put the 8" @ 25yd group person on the 3yd line and tell them to dump the magazine as fast as they can, I bet they keep 'em all on the paper, probably in 6-8". So, why did they only hit the entire person one out of three? Must be something missing outside of raw marksmanship, since they have demonstrated better marksmanship repeatedly...
If I had 1000rds to teach someone how to shoot their pistol, 1st I'd redefine the goal. My goal; 1000rds to teach them how to survive a gunfight. I'd teach them how to shoot their pistol mainly via dry-fire. Confirm and refine with up to 500rds on the range. Once we've established they have the raw marskmanship skill to get the hits required, I'd use the remaining 500 working on progressively more stressful drills primarily at close range (some from cover and also at extended ranges). I'd also trade 200 of the live rounds for 100 Simunition FX for FoF, 50 blanks safe at contact range for extreme CQC striking/shooting, and 50 frangibles for a shoot house. The high-stress drills and FoF training is what will help enable them to tap into more of their raw marksmanship ability under stress. It is there, but hard to access when the first time you try to shoot a moving person who is shooting back, is the real thing. (Not the marksmanship problem of it, we can move while shooting moving targets at a range, the stress of it)
Progressively more realistic and stressful training is what helps bridge the gap between square range performance and combat performance. The first few times you suck. Next few get better. So much so, that our best trained Tier 1 units have little degredation between their square range and combat performance.
The guy who killed Bin Laden scored two rapid head shots in combat at night against a moving target surrounded by no-shoot targets. If all he did was train on static targets at a range, with no high stress FoF or shoot houses etc, forget it! It wouldn't matter what groups he shot prior and how far. He also had so much combat experience he stopped even getting adrenaline dumps in firefights. The goal of training is to simulate that as close as possible since most of us will thankfully never get enough real combat to be good at it.