When they went back three days, they seemed to go in a bubble that took all their problems with them. Joe Tormolin was still dead. And they can't really prevent the problems that occurred (damage to the warp engines, hangovers...) because that all went back with them too.
They went back in time from the universe's point of view, but kept all the bad experienced they'd just had. It's not what you have in mind when bad things happen and you wish you could go back.
"Otherwise, wouldn't there now be two of the Enterprise and crew existing on the same timeline?"
Right! When the Enterprise went back in time, it would suddenly appear in its "experienced" state and disappear from where it was the first time around. That ship would vanish. And yet that wipes out the having of the intoxicating experiences at Psi 2000 which the crew remembers. So it's a paradox.