Ugh... then how did he took Caldari Prime?
As for me, Executor is corresponds to the head of executive branch of power, and this implies control over army.
Heth does not have actual control over the Navy itself.
Ultimate authority with the Navy rests with the entire CEP as a cooperative entity,
not him alone. The CEP directs the War Council, which in turn directs the group of State military forces such as Army, Navy, Marines, and other black ops groups. Keep in mind that the Caldari Navy has not once acted against the orders of the CEP. It was Templis Dragonaurs on the scene against SuVee during the live event, not the Caldari Navy.
Heth was able to make use of the Navy for other operations using his
influence, not actual authority. He convinced the CEP to green-light the operation against the Federation during YC110, for example. So the War Council drew up plans to invade, and the rest is history. Same with the purge of DUST soldiers. Everything the Navy does must be approved by the CEP. They are not Heth's lapdogs.
There have been multiple chronicles and chapters in the books that clearly show the Navy does not answer to Heth. The highest ranking and leading officer of the Caldari Navy,
Admiral Mininela Erinen herself, directly resists and threatens Heth by often reminding him that he does not give her orders.