I think what you're saying is that a character with this ability has different outcomes than one who doesn't. However, the character in and of himself is still making a binary attack; it's just that instead of hitting or missing, he's hitting or sort of hitting. This is not like the skill examples above where one roll made by one character could have three or more distinct results.
For what it is worth, you can still fail even with this ability (though this does not directly address your three-results reply, which I think is valid and I wouldn't mind three results).
Anyway, here are just a few ways you can fail to damage your target even with this option:
Player: I move next to the Kobold and try to hit it with my sword, doing at minimum my Strength damage with the attack.
DM: The Kobold had readied an action to move as anyone tried to kill it. So he moves out of the way, and you fail to do any damage.
[Next Round]
Player: I move next to where the Kobold is now and try to hit it with my sword, doing at minimum my Strength damage with the attack.
DM: Make a reflex save to avoid falling in the hidden pit trap you're now standing on that is next to where the Kobold moved. If you succeed you are in the space behind the pit, but still fail to damage the Kobold as you're not next to him. If you fail, you fall in the pit and take damage, and fail to damage the Kobold.
[Next Round]
Player: Dammit this bugger is really slippery! OK I made my save so I move again to where he's now standing try to hit it with my sword, doing at minimum my Strength damage with the attack.
DM: You draw an opportunity attack from the Kobold you pass on your way to your target Kobold. He hits you with a tanglefoot bag. Even if you make your save, you won't have enough move left to reach your target Kobold to try and hit him with your sword, and fail to damage the Kobold.
Player: Screw it! Let someone else kill that Kobold. Where is this new guy who hit me with the bag?