I was visiting Illinois last week and I had the chance to catch a playoff game from the town I used to live in. Below is the play and the resulting call. It did not seem right to me, but I have only officiated football for two years and I wasn't quite sure when asked by others. Your response would be appreciated.
************************************************** *****
Team A has the ball on their 30 yard line. A1 sweeps right and is stripped by B1 (defensive back).

B1 heads for his goal line running by the sideline. Team A player hits B1 at about the 2 yard line. The ball pops out of B1's hand and goes through the back of the end zone without anyone in possesion of the ball.

The white hat signaled a touch back and put the ball on the 20 yard line. (Here is the question part of the play) He gave the ball back to Team A on the 20 yard line.

Now I can understand the touchback and placing the ball on the 20 but shouldn't Team B have gotten the ball?

************************************************** *****

Nope. Think of the same play, only A is on the 5 and A1 fumbles through the end zone and over the end line. You wouldn't give it back to A at the 20 and say, "here - try again". Fumbling into the end zone and having it recovered by the opponent or having it go OB or over the end line results in a touchback and it's the other teams ball. Kind of a big disincentive for fumbling into the endzone.

Thanks - That makes a lot of sense.

Very basic, who has possession of the ball?

At the time of the fumble the ball is in player and team possession of B. It remains in team possession of B as it crosses the endline of B's end zone. Therefore, it is a touchback.

If the ball had not been possessed by B and had bounded into the end zone and over the endline it would have been a safety.