I'm assuming it means it increases how much the heal gun heals, just because the tanks health increase doesn't say "Increases Tank's Health" It says it increase health. So that is my assumption.
But it does have it Capitalized, which leads me to believe it's the name of the class and not the weapon. I assumed that when it said "increases health recovery" that was when it meant the healgun healed more.
Support passive: Rank 2: Add's aura that gives bots more hp/fire rate. Increased health recovery for support. Rank 3: Increase's supports max health. Case closed.
I thought "Increases Support Health" meant that it increased the health of the Support. What's ambiguous?
I read it as increasing the healing rate of the Healgun. In other words, the support will heal his teammates/turrets at a faster rate than before.
It's kind of pointless, since you don't need a lot of health when your firebase is killing everything for you.