Just like you say, Romo missed 10 games or more in three season - 2010, 2015 and 2016 (I think you mean 2015 when you posted 2014 above).
The last five years is the period where Dallas finally started to draft well and build a young core. In that period (with Romo and Garrett) they went 8-7 in 2013 and 12-3 in 2014 for a record of 20 - 10.
So when the team was drafting well and Romo was healthy, Garrett went 20 - 10. That's the opposite of your original point that Garrett coiuldn't win with Romo.