Defeating an at Home via a Burglary gone wrong

[Gamling the Old]

I have defeated a Smaug at Home with a character that was using Burglary to get in but failed the roll.

Does this remove Smaug from play ?

Opponent claims

"When a Dragon manifestation (e.g. Ahunt, At Home, Roused, or the creature manifestation of the Dragon; Dragon automatic-attacks are not considered manifestations) is defeated or otherwise removed from play, all other manifestations of the same Dragon in play are removed from play..."

So defeating the augmented (via Burglary) automatic-attack that "Smaug at Home" grants does not defeat the "At Home" manifestation itself — only a direct defeat of the manifestation card would (e.g. facing it as a creature).

To me his argument is strange as the Samug at home says "The Lonely Mountain has an additional automatic-attack: Dragon — 2 strikes at 18/8" so you can never defeat it as the Creature ?

[Gamling the Old]

Related

If Smaug is at Home and I move there. Opponent plays unabated by Malice.

Somehow I manage to defeat the Unabated attack, does this mean I killed smaug and lonely mount has no autmatic attacks any more?

[Konrad Klar]

Dragon automatic-attacks are not considered manifestations of any unique Dragon.

So true as true is that Smaug Ahunt is a manifestation of Smaug, but the attack from the Smaug Ahunt itself is not.
But still, the only way of defeating the Smaug Ahunt is a defeating of the attack from the Smaug Ahunt.
The only way of defeating the Smaug at Home is a defeating of the attack from the Smaug at Home.

Somehow I manage to defeat the Unabated attack, does this mean I killed smaug and lonely mount has no autmatic attacks any more?

Copy of the AA from Smaug at Home is not AA from Smaug at Home.
So no.