No the healer doesn't lower anyone's enmity, the tank is just blaming it on something other than his skills, what could've been different is the use of offensive cooldowns like FoF and was the tank in identical gear? Same weapon and accessories? The other tank might've had str ACCs instead increasing his enmity.

If I'm not wrong enmity is equal to damage dealt, Shield Oath multiplies enmity by 2, Savage blade by 3, and RoH by 5 so if the other tank had a higher str and RoH right after him he would get aggro back.

@Dotsusama, I believe you mean Bloodbath and not BfB