No, I believe the Burned Tower theory refers to the first three Eeveelutions (Flareon, Jolteon, and Vaporeon), and the fact that they perished in the fire and were brought back as the three Legendary Shadows of Ho-oh (Who the game is about...) which were Entei, Raikou, and Suicune, all of the same types as the Eeveelutions. Entei and Flareon are fire, Raikou and Jolteon are both electric, and Vaporeon and Suicune are both water! Plus, Entei, Raikou, and Suicune are all in the Burned Tower! The game also mentions that
"Three Pokemon perished in the fire, and a rainbow Pokemon brought them back."
The "rainbow Pokemon" is obviously Ho-oh, who has a special connection to Entei, Raikou, and Suicune.
I like your theory, though. The only things wrong with it are:
- Articuno is an ice type, canceling out the Burned Tower theory.
- Articuno's beak is too short. (agreed.)
- Ho-oh, (not what you'd think) has no special connection to the three Legendary Birds.
Even though the Burned Tower was originally the Tin Tower in Gold and Silver, Lugia's tower, it specifically states that Ho-oh saved them.
Good observation, though! Good question! Hope I helped! :D