This is not aimed at you but I am using your quote below as a general point from which to expand.
roughly baseball-sized 5-shot groups at 100 yards with Remington factory loads.
For a battle rifle that is pretty darn good with factory loads - most, if not all battle rifles were designed for MOM or Minute of Man type accuracy and no better. The modern military of the day knew that the marksmanship of the average rifleman was only going to be of a certain standard so there was no point giving a precision target rifle to a grunt who wouldn't put it to proper use; that little preiveledge was reserved for the hand picked heavy barreled rifles given to snipers.. Any round hitting any portion of a soldiers body was going to have the effect of stopping them, killing them or slowing them down and Minute of Man is exactly what these rifles were designed for ... however.
When trials were first conducted by the British on the No5 Mk1 rifle they trialled it side by side with the No4 Mk1. It was quickly found that the No5 Mk1 was as accurate as the No4 out to 600 yards and thus the effective range was given as 600 yards. The British also trialed the No5 using a standard No4 butt stock and found that accuracy improved yet even more - this is another discussion again. The reality of Jungle Warfare however is that the general effective range in which the rifle was to find practical use was 300 yards and under. The No5 can be made very accurate out to 600 yards given care and tuning of the stock and working with hand loads.
There are many reasons why people pick up an Enfield and claim them inaccurate ( Most do not find them so ... ) - many of these rifles have their original barrels, most of which are over 40 years old and more and have seen a few battles. In the Commonwealth Military all Enfield rifles saw regular inspections by REME base and field work shops ... these inspections were usually three times a year where they were continually checked and assessed for tolerances. In an Enfield rifles post war life they have likely missed about 40+ years of maintenance and care which leads us to why an Enfield rifle may not be as accurate as it could be.
1 - The furniture/stock has dried out ... Enfield rifles were treated with BLO ( Boiled Linseed Oil ) which was their natural and original finish. Over many years of sitting in storage the bedding on an Enfield can be completely altered from it's original state when it left factory or met last inspection. The receiver and barrel can often seem loose as a result of shrinkage. There are means and methods of fixing this and often times giving the stock a drink of Linseed Oil will allow it to return to it's former glory whereupon it will hug all its metal parts like it should. You will find that even this small act a benefit to your groups.
2 - Bore - If you take a rifle barrel that has seen a world war and then 40 years of shooting post war you are more than likely going to have a barrel showing it's age. Original Enfield barrels might well be showing signs of throat erosion and wear to the leade and also wear in the bore itself. It may not be hugely out of spec but before anybody claims their Enfield inaccurate they might do well to slug the bore first as they are likely to find they need to move to handloads with a slightly larger projectile.
I can't count the amount of times I've advised new Enfield owners to do this and the fliers they once had at the range disappear in the wake of very tight groups.
3 - Bedding - An Enfield rifle is a subtle bit of kit and requires a bit of care and craft in order to extract the very best from it. Understanding the black arts to bedding an Enfield is imperative and this is no less than the Commonwealth Armourers who inspected the rifles would have done in their days when new. People need to understand they are dealing with old battle rifles and not out of the box modern factory jobs. I shoot along side many Military Service rifle owners and these rifles can shoot the eye out of a bird flying when cared for ... let's not forget that it's also the nut behind the bolt that has much to say on accuracy also.
If anybody picks up a 40+ year old car that used to be high performance you can bet your life it won't run like it did when new ... it will need tuning and TLC to get it running at optimum again. If you do this it will repay you in kind with performance but you can't judge the performance based on 40 years of neglect and zero maintenance.
If anybody wants to know more about Enfields and getting the best out of them then by all means visit the forum ( http://www.surplusrifleforum.com/viewforum.php?f=27
) there's plenty of top shooters running Enfields there. Sorry for the long winded post but Enfields are a passion for me and there are plenty of issues and misconceptions about them that often require exposition.