That was not a blown call. The ruling of touchdown was incorrect and was overruled with the a challenge. What you left out, however, was the facemask penalty during the run. The Bears accepted the penalty which wiped out the play completely.
If I remember that explanation of the Carolina challenge right, the ref specifically said that the ball had been fumbled through the end zone after the runner lost the ball before breaking the plane of the goal line; which without the face-mask penalty, would have resulted in Carolina ball at the 20. With the face-mask penalty, accepted by Chicago, the penalty wiped out the play, half the distance to the goal was marched off from the previous spot (the Carolina 7), and the ball was placed at (officially) the Carolina 3.
You are correct, my bad.
However reviewing the play, the runner was as guilty of hanging onto the facemask of the tackler as the other way.
Speaking of bad through-the-end-zone fumble calls, how about that one from Saturday? I don't know what replays the refs watched, but the ones I did clearly show the ball gone from Champ Bailey's hand (and ultimately through the end zone) before he went out of bounds.