The reason Balrog was able to borrow this fleet had something to do with his identity with the Anomalous Management Division.
But mainly because of his bad temper and eccentric personality, no one wanted to offend such a lunatic.
Moreover, the nature of Rhodiola rosea's team also matched the fleet's combat objectives, and they were all located in the Asteroid Belt.
These three factors combined allowed him to borrow the fleet in his personal name.
However, even so, he couldn't bear the consequences of the fleet's destruction—he would still have enough wiggle room even in a pyrrhic victory.
Because of this, he eventually lost the will to live and insisted on a duel with Qu Jianlei.
Of course, with this guy's arrogant personality, encountering such a fiasco, he likely couldn't calmly accept it.
Thus, putting everything on the line for a chance to save face wasn't surprising.
Additionally, Qu Jianlei specifically looked into the origins of those two Armed Merchant Ships.
