The '03 is made so the extractor can flex and the bolt can be closed on a single round dropped into the chamber. This without damaging the extractor at all.
This was needed due to the Magazine Cut-Off system built into the rifle.
The Mauser 98 extractor was not designed to do this as there is no Cut-off on the design.
If you force it, the bolt can be closed on a round in the chamber but it puts a lot of un-needed stress on the extractor claw as it is not designed of it.
It is possible to reshape the front edge of the claw for it too close easier on a loaded rd. But the flexing action of the body of the extractor is still more than the overall design is made for.
As far as the controlled feed,,That is the round being pushed out of the magazine by the bolt and forward to be chambered.
The bottom portion of the bolt face is open,,no encirclement of steel as in a Rem700.
It is open so the cartridge head can slip up onto the bolt face as it rises from the magazine. At the same time the case head extractor groove slides behind the bolt's extractor claw.
Should the round be 'short stroked',,it will still be extracted and ejected from the rifle as the extractor claw has a hold of the case .
On a Push feed system, the round out of the magazine is mearly pushed forward by the bolt face towards the chamber and into it. Never having a purchase/hold of the round. That occurs only when the round is fully chambered and the bolt fully closed. Then and only then does the small spring clip extractor snap over the case head extractor groove.
When fitted up, a controlled feed bolt should have the extractor claw just barely touch and hold the case while on the bolt face.
That's the gunsmith's way of fitting up a good rifle. I'd expect most new Military rifles of decent mfg had come down the line the same way.
But with 80 to 100+ yrs of use and wear in sometimes horrible conditions, that narrow edge of the claw extractor gets worn. Sometimes severely. But it can still do it's job.
Also ammunition specs can be all over the place esp the depth of the extractor groove on the case. A couple .000 too deep and case will seem to be a loose fit under the extractor. But again the system will work just fine.
Placing a round onto the bolt face and rotating the bolt assembly to put the extractor claw at 6 o/clock will often let the round fall free of the bolt .
That can be due to any of the above. Plus the simple geometry of the case being unsupported on the boltface and the 6 o'clock extractor position is now nothing but a pivot point for the round to tumble from.
Springfield and Mauser bolts feel 'loose' in their actions,,some way worse than others due to wear. Some are just sloppy fit due to 'gunsmithing' over the yrs in trys to make a better sporter.
A first rate Oberndorf Sporter is a very smooth working action as is a Nat'l MAtch 1903.
The design of the Rem700 adds to it's smooth working bolt.
No added 3rd Safety Lug or Bolt Guide Rib on the bolt body keeps it just a plain cylindrical body.
No Stripper Clip guide cut-outs on the rear bridge.
No Ejector /Bolt Stop cut on the left side of the recv'r at the rear
The 2 opposed locking lugs are the only slots needed in the action for the bolt passage.
Plus the rear recv'r bridge is a bit longer than most of the Mauser/Springfield actions, That aids in supporting the bolt for smooth operation when fully retracted.