TBSG
As you bring up doctrine - I am afraid that this is not a 'light blueism' but is doctrine. JWP 0-01.1 (UNITED KINGDOM GLOSSARY OF JOINT AND MULTINATIONAL TERMS AND DEFINITIONS) is clear that Air Power is
The ability to project military force in air or space by or from a platform or missile operating above the surface of the earth. Air platforms are defined as any aircraft, helicopter or unmanned air vehicle.
It doesn't matter what Service or arm operates the air platform, or what component commands it - the fact that it is an air platform makes it part of air power. Therefore the Army Aviation hele-tele (and other airborne survellance assets) working over the Falls Road were, doctrinally, air power.