I think the head sizes must be 3/16" and 5/16", respectively, but I get your point.
I don't understand your statement? The manfactured heads are smaller not bigger!
Lockheed standard (LS) rivets have a manufactured head one rivet size smaller than MS rivets.
When you install a 1/8" LS universal (protruding) head rivet you use a 3/32" rivet set (die).
When you install a 3/16" LS flush rivet, the countersink in the skin is the same depth and diameter as that for a 5/32" MS rivet.
The LS manfactured rivet heads are one rivet size smaller than there MS counterparts.