Wouldn't it be nice or interesting if Stark knew of a Skrull infiltration and the purpose of it was to registration was to ferret out the Skrulls.

Part of the registration process was to detect if someone was a Skrull.

Could be a nice reason that Stark would want the body of Captain America under Shield jurisdiction as it could turn out that Cap was a Skrull.

With the major scientists on the side of the regs, maybe they came up with a process to detect the Skrulls.

Those that didn't register cannot be told about the Skrulls because they might be Skrulls.

Could be interesting if somewhat true.