There is no "built-in" browser from the point of view of Aquamail.
Even the "Chooser" is Android's function, Aquamail just passes Android the "intent": "A website needs to be viewed" and the URL.
If there is more then one browser, and no default is set, Android will offer a choice of browsers that are capable of handling that intent. If there is only one, - it will be used even in the absence of default setting.
So, either there is yet a different related default (for the intent different from the one you've cleared), -- in which case you'd need to clear that one, or there is something odd in your launcher/rom/ OEM-specific environment.
What is your phone, Android version, and the launcher? -- That information might give some clue...
