IMO, there is a difference between going to the ground in order to catch the ball and going to the ground after you catch the ball. If the first instance, it would seem that you have given yourself up at the point the catch is complete plus element of time & football move. Not necessary for defender to "down" you. In this instance, i would view the ball coming over the goal line as part of the catch, time & football move & thus rule TD.
In the second instance, say you stretch out for a ball & caught it with both feet off the ground stumble multiple steps & go to the ground. I would say you haven't given yourself up and that any move to further advance the ball before being downed by an opponent should count.