Sprinkler In-Between 6-in Catwalk & Ceiling Gap?

We have a school theater project where there are three catwalks (each 3'-9" wide) above the seating area that have cloud ceilings that completely cover the bottom of the catwalk. The ceilings are within 6" below the bottom of the catwalk.

There is ceiling level sprinkler protection and sprinklers dropped into the clouds.

I do not think that a line of sprinklers is needed in between the bottom of the catwalk and top of the cloud. The A/E is saying that three levels of sprinkler protection is required in this situation (ceiling, catwalk, & clouds).

Is sprinkler protection required between the catwalk and ceiling below? 

Any help either way, for or against adding the extra line would be great.

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