[Spoiler] Evidence to prove Aquila attacked the Providence?

Hey everyone,

I read somewhere that the ship that attacked the Providence (the one you are on as Haytham) was actually the Aquila. Now, it doesn't state this any where in the game (to my knowledge) and it is very hard to get a clear image when the ship is attacking to identify specific features on the ship (such as the eagle at the front). Here is the "evidence" I have so far:

• Haytham was on the Providence in 1754.
• The ship attacking the Providence was allegedly struck by lightning and had sunk during the storm.
• Story of what happened to the Aquila "In 1754, after being engaged by a Templar warship, the Assassins spread the word that the Aquila had been destroyed in a storm. In reality, she had only sustained minor damage, and was soon refitted for combat. "

Is it to far fetched to believe that the Aquila was the ship attacking the Providence to kill Haytham?