You're close.
There is a law that prohibits what we call "parallel construction." That means, effectively, you can't be investigated for the same crime by two different authorities at the same time.
If there were already active investigations into Clinton and others - then it would be necessary to limit the SC's scope and force prosecutorial referral. IE - any discovered evidence of a crime would be referred to the prosecutor(s) responsible for those respective investigations.
Congress gave the SC massive amounts of authority in the beginning, because they wanted to prohibit investigations into the DNC, Clinton, Russia, etc. However, the SC couldn't be expanded to take priority over existing investigations - it would have that authority curtailed. Further, if the nature of those investigations was secretive, then the fact the SC's power had been curtailed by ongoing investigations into the same would also be kept classified except to the one handling the SC. IE - Mueller and RR.