Accuracy is a relative term.
And it can be complicated at times.
Yes,, ammo is but one component of accuracy.
The gun itself, the ammo, the shooter, all are important.
If the gun has issues,, no ammo or shooter ability will fix it.
If the shooter isn't doing things correctly,, well, you can easily get mixed results.
But the ammo as noted above can have a "sweet spot" for accuracy in a particular firearm. That's what most handloaders strive for.
If the gun has bedding issues,, that can be corrected fairly easily. If the barrel is worn out,, a replacement is necessary.
A shooter is also a variable factor. I've seen many a target by a shooter claiming to be "good" yet,, put them against a real shooter & they would be very embarrassed.
Handloaders, (vs a reloader,) strive to find an ammo that matches the firearm. They make the brass as uniform as possible. They select several different bullets, powders, & primers & start building test ammo to try out in that one gun. They may build 50 or more different combinations of components to find what truly is accurate in a firearm. Then they will zero in on what they can do to fine tune that ammo & gun to achieve it's full potential.
The 2-3 inches at 50 yds would not be acceptable to me by MY standards. Maybe somewhat in a handgun, but again, that depends upon a few other factors. But a rifle,, not so much.
And older gun like the Swedish Mauser you mentioned should still be capable of 1-3 inches at 100 yds if it's not shot out, rusted out or other gun issues.