Heard the old VP of the refs talking on the radio today. He was asked similar questions. The reason they say that control has to be maintained throughout the whole process of the catch is how do you define when the catch is made? On any catch you could land on both feet in bounds (a complete pass), but when you fall to the ground, the ball could come loose, making it an incomplete catch. If it wasn't defined as a "process" then there would be ambiguity as to when a catch was made, which is not something you want in a rule.
With respect to a runner crossing the plane of the goal line and then losing the ball, the ref said the difference is the runner already has possession of the ball, so when he crosses the plane, its a touchdown. With respect to a receiver trying to catch the ball, he is trying to gain possession, so it doesn't matter if he is across the goal line or not until he has possession, which occurs at the end of the process.
So technically the correct call was made, but that was a touchdown and the Bears should have lost. I am a Bears fan too. Maybe next time the receiver will tuck the ball away rather than rushing to get up and celebrate. If he just would have fallen down, there would have been no controversy.