Accuracy means different things to different people.
For some, hitting a soda can sized target means they're very accurate, some think hitting a clay pigeon sized target is accurate, and some may feel hitting the tip of a match or cutting a card is accurate... If you are of the latter persuasion then you are more likely to understand, know and feel the difference.
I've had many friends who couldn't shoot a highly tuned sniper rifle any better than a cheap Walmart gun... So yeah, shooting accurately IS in the shooter, not just the slingshot.... Because I can tell you for a fact an actual sniper can shoot a tuned sniper rifle much more accurately than he can shoot a Walmart special.... But here's the thing, he/she can also shoot the Walmart special rifle better than most people can shoot the $5000 tuned sniper rifle as well.
Most likely only in the hands of what may be considered an expert will the true differences be shown.... And yes I do know there are some experts than prefer OTT over TTF... and then again there are also a lot of experts who switched from OTT to TTF after giving it a fair try... Maybe they're wrong, maybe they're right... But I have seen a trend of more and more TTF shooters shooting in the top ranks of tournaments every year.... and more and more winning as well.
When you shoot a slingshot, any slingshot, you have many variables to deal with... stance, sight and band alignment, cant both sideways and to and fro, anchor/ no anchor, grip firmness, arm straightness and rigidity, draw weight to ammo size, and then finally target focus versus sight alignment while making sure all the other factors are correct..... Then release, release like holding a butterfly? Hold in front of ammo, on the ammo, give a tug or pull backwards as you release? And all while trying to breathe in such a way as to not mess everything up....
And I've probably skipped over a few variables as well...
In my opinion, the reason TTF is more inherently accurate then OTT is that TTF is a little more forgiving of minor variable infractions than OTT is.... Meaning, if I don't center the ball exactly in the pouch and my release is the tiniest of a fraction off, the ball is still going to go more inline with the bands than if you did the same with OTT...
So what I'm saying, in a nutshell, NOBODY is perfect.... EVERYBODY makes tiny, minor mistakes in at least some of the variables.... TTF is a tiny amount more forgiving of that.
Now, of course if you're a beginner, or even someone who's been shooting for ages... and you don't have real good control over most of what can go wrong... you'll probably never notice a difference in one versus the other... and in fact may complain that TTF gives you forkhits, when it's your problem release that's the thing, not TTF...
Probably the only things you'll notice with TTF is less handslap, even with mismatched ammo to elastics, or that it's a little noisier because the band impact on the frame.... Regardless of what you do notice, there is a difference in accuracy as well, you just have to be at a level of expertise that most people won't ever achieve to fully appreciate it is all.