Well, having been in an (German) Army Helicopter unit the "tight interaction" between ground troops and flying units requires stuff that fixed-wing aircrafts are not really good at. They can't stand still in the air, the cant land vertically in tight spaces (without burning people with jet exhaust like a VTOL jet would) , etc...
Basically anything fast/long-range/big is usually handled by the air force planes (or helicopters), while slow/agile/close coordination with ground troops is handled by the army air corps. Usually with helicopters, although some planes are used by armies, like the Britten-Norman Defender by the British army.
Very true, and try getting the Air Force to support a JAAT (speaking late coldwar here) without 30 days notice or some BS. If you needed close air support, the Navy and the Marines needed to be nearby.