No, this is not about being able to kill mobs with the tag while I'm in Creative mode.

Minecraft wiki says (under "Tags common to all entities"):

Invulnerable: 1 or 0 (true/false) - true if the entity should not take damage. This applies to living and nonliving entities alike: mobs should not take damage from any source (including potion effects), and cannot be moved by fishing rods, attacks, explosions, or projectiles, and objects such as vehicles and item frames cannot be destroyed unless their supports are removed. Invulnerable player entities are also ignored by any hostile mobs. Note that these entities can be damaged by players in Creative mode.

I tried using a fishing rod on an Invulnerable mob, and it worked even in survival mode.

Version history of this issue:

13w36a (1.7): /summon added, so this was the earliest I tested.

13w36a-14w08a (1.8): Invulnerable mobs completely damage immune, even to creative players, and fishing rod doesn't do anything.

14w10a: "Players in creative mode can now damage entities even if they are flagged invulnerable."

14w10a-15w35e (1.9): In creative, the fishing rod does "pseudo-damage", including knockback, on initial attachment, and pulling works. In survival, the bobber passes through. This is the period I believe is showing the intended behavior.

15w36a: "Most entities can now be pushed by other entities... The same class of entities are now 'magnetic' to the fishing rod bobber, and in the case of mobs/players will no longer suffer from knockback or pseudo-damage."

15w36a-present: The fishing rod can be used on Invulnerable mobs even in survival mode.