The head of the SID wouldn't have the power to decide something like this, I think; essentially, they are the head of a specialized police department, not someone who makes far-reaching policy decisions (as we see later on in the series). So IMO this kind of decision would go to someone considerably higher up, more on the policy side of things rather than the executive. I could imagine this might have been handled by Zhao Xinci's predecessor in his current role, and/or the previous minister. The head of the SID might be asked for their opinion, but no more than that.

BTW, I always assumed that the SID and the Envoy's agreed-upon role on Haixing were established at the same time, as complementary counterweights.