1. Tyrion appears to be wrong in his memories here. At least Gawen was executed by the King himself with Blackfyre, not by his Axeman.
2. Some members have issues with the statement "Open Rebellion". As far as Tyrells are concerned, they are in rebellion. They have sent forces to Daenerys. Cersei isn't that much of an idiot to delude herself that Tyrells will accept her rule after her murder of Lord Tyrell and his children. Daenerys isn't going to waste her time in stopping for camps. She has to reach her destination fast and strike hard, due to rules of logistics. Tyrells don't even need to hide their rebellion as Cersei's rule is unrecognized by great lords and there is no danger from the remnants of Lannister army, battered and tired from a long war.