Just to be disagreeable (and maybe add to the discussion), I'd vote no on requiring 4" openings. If the building is an S, and especially since it is behind a security barrier/fence, I'd say your stairs fall within exception 4 (1015.4, 2015 IBC) no matter what door they lead to within the S building.
From the Commentary: "Exceptions 3 and 4 address areas where the presence of small children is unlikely and often prohibited. Guards along walkways leading to electrical, mechanical and plumbing systems or equipment and in occupancies in Groups I-3, F, H, and S may be constructed in such a way that a sphere 21 inches in diameter will not pass through any of the openings."
How high are these stairs? I'm not sure that'd effect my opinion either, but this call may be a lot easier for some to make if this is a flight of 3 or 4 steps vs. a flight of 10 or 12.. And also, like pcinsp said - if you're less than 30" total then you don't have to provide anything.