In NFL terms "impetus" comes from the last team that had full possession of the ball, not the last team to touch it. That's why in a punt "impetus" comes from the punter.
The basic reality is simple, when a fumbled ball bounces out of bounds possession goes to the last team that had it at the point where the ball crosses the line. Basically the boundary is considered a 12th for whichever team last had possession, when the boundary "gets" the ball it goes to that team. When a team starts a play with possession of the ball ends that play with possession in their own endzone it's a safety (except for certain incredibly convoluted possibilities that involve at least two turnovers and are outside the scope of discussing this play). Dallas started with possession, fumbled, neither team recovered the ball even momentarily before the ball went back into the endzone and then out of bounds, so the step by step result is thus: Dallas' ball at the spot the ball went out of bounds, oh that spot was in their own endzone, that makes it a safety. You're not going to get a free twenty yards for fumbling the ball and not recovering it with one of your 11 guys on the field, unless by some strangeness the ball bounces forward 20 yards before going out of bounds.