Flexor the Mighty!
18/100 Strength!
I was referring primarily to the 5e Fighter's Rally maneuver and the 4e inspiration for it, the Warlord's Inspiring Word feature. Both these powers are fluffed as delivering a rousing verse or two that boosts the target's morale. To me it doesn't make a lot of sense that an inspiring phrase (explicitly non-magical ones) can heal debilitating wounds of allies.
Delivering first aid is a different story. You are actively attending to the target's physical injuries. It may be a tad unrealistic since first aid in the real world tends to have slower effects, but it is more of an acceptable break from reality that healing wounds by shouting at someone.
HP do not purely equal physical wounds. For a high level PC I'd say most of them are not actually cuts and wounds.