I'm not sure if that is correct. Both the S-300 and the Aegis SPY require fire control radars and channels for missile guidance. The Aegis, like everything else, is limited by the number of channels you have for each missile.
First, lets clarify the term fire control radar vs. illuminators. Both terms tend to be used interchangeably, but FCR is more of a broad term that includes a radar that is capable of giving fire control quality tracking information. Basically that means the radar is illuminating the target rapidly to get a stream of returns. An illuminator is in effect, a radar flashlight. For the target, both are in fact similar, the target is getting illuminated so frequently it may appear continuous.
The S-300 needs to keep its main phase array at the targets so it can provide the missile with FQ information. Only when the missile is at terminal range will the ground unit get the relayed responses from the seeker.
The interesting thing about this is that it can be decoy proof, because ground computers are much more powerful than whatever you can put inside the missile, and they can sort out the radar returns and determine better which is the real target and which are the decoys. The ground computers can also compare data between those received from the seeker and from the ground radar.
As for AEGIS, its a basic that any missile requires a seperate channel on each own, especially if you're multiplexing at the terminal basket.
Let us say you're engaging 8 targets. You got four illuminators, and 8 missiles on the air, with 8 channels on the ship. Before each missile reaches terminal seeker range, they each have to be guided via datalink, and for each missile you must have a separate datalink channel, otherwise you don't want them to jam each other or have Missile A get instructions that were meant for Missile B.
4 missiles have reached the terminal point, and at this moment, the illuminators are fired up lighting the targets. At this point, these four missiles can leave their channels, which can leave the channels open for four new missiles to be launched. 4 targets are destroyed, another four has reached terminal range, and the illuminators switched their targets to the next four. At this point the second set of four missiles that were being midguided now go into terminal and leaves their channels.
For actively guided missiles, the principle is the same. You need datalink channels for each and every missile, and the channels are maintained until the target is at the seeker terminal range. The real difference is what is illuminating at the terminal range. The radar on the seeker does not have the same emitting power and resolving aperture compared to ship radars by magnitudes. Thus ARH missiles like SARH, require midphase help and guidance via datalink channels.
The real difference between S-300/PAC and AEGIS is that the S-300 needs to keep the channel all the way until it hits the target, where a SARH or ARH missile can leave the channel sooner so that you can rotate different missiles on the same channel faster. Now the question is whether which method, SARH or ARH, can allow the missile to leave the channels sooner.
At minimum range engagements where targets are too close, you can set the seekers to go active or start illuminating as soon as the missile bends over. At these ranges you don't need mid phase guidance since the targets are already at seeker range.