For my part, I don' t recall ever saying a longbow, or any bow, is super accurate. They aren' t--accuracy is in the shooter. Put a match grade rifle in the hands of a novice, it won' t win any competitions. All of the " good" archers that I know (Bill Leslie is probably the best known) can shoot pretty much any bow you put in their hands accurately. I' ve seen Bill take a borrowed selfbow and borrowed arrows (that weren' t matched to the bow for his draw) and still shoot dang good.
I have owned a 21st Century longbow--it was a good bow, very quick, but one that felt much like a recurve to me. I' m not downing the accomplishments of those who shoot them, but again I don' t believe for a minute it was the bow. I believe Keith Bain is shooting a 21st Century now, but he has won numerous tournaments with other bows. Sponsership can go a long way--ever notice how many of the big-time compound shooters are winning with Matthews bows nowadays? (just pick up an archery magizine and read the ads and you will see--lol[X(])
Heavy risers, cut to center/past center/centershot riser, etc. do make a bow more forgiving, but that is different than making it more accurate. Howard Hill was accurate. Ben Pearson was accurate. Fred Bear, the Wilheim brothers, etc. were accurate. Byron Ferguson is still accurate.
I have by no means " mastered" the longbow, but I am usually an above average shot. I have competed with recurves also, and won with them, but I am much more comfortable with a longbow. Maybe I haven' t shot the right recurve....or maybe a lot of recurve shooters haven' t shot the right longbow!

I personally know one fellow who is an excellent shot, and has taken many state level competions along with gobs of smaller shoots with his recurves. He used to fuss and cuss at every longbow he saw--there was no way he would ever own one of those things, and couldn' t understand why anyone would want to shoot one when they could be shooting a recurve. Well, one day he got his hands on the " right" longbow, and now he owns it. He' s a dang good shot with it too.
One other thing that hasn' t been mentioned (sorry for getting so far off the subject benhuntin) is the difference between shooting in competition and hunting situations. Most all serious target archers have a particular stance, bow straight up, feet placed just so, etc. Take this away from them and most fall apart--not good in the woods. I know one fellow who has taken more game than most folks have seen on the Discovery Channel who says he cannot shoot 3-D targets to save his life (I haven' t seen him shoot)--most with a longbow, some with a selfbow. A few years ago (I believe it was on the Outdoor Channel) an Olympic Champion archer (Jay something?) missed a gimme shot on a deer on camera.
Ok, enough rambling. Again I say, don' t worry about opinions, go with what works for you. Recurve, longbow, flatbow, selfbow--whatever. Archery is 90% mental, and confidence in your equipment is vital. Shoot what works for you.
Chad