This is a poker theory / philosphical question: which takes precedence, Slanksy's Fundamental Theory of Poker or the use of hand ranges?

Example:
You are playing a headsup cash game against a maniac villain who pushes all-in with every hand blind.

You are dealt Ace-King.
You call.
Villain turns over Ace-Ace.
Let's say you lose the showdown for giggles.
Did you make a mistake and why (or why not)?

I'd prefer a decisive yes or no (with reasons).
If this is an easier question you may answer it:
Does your call show long term profit?

The point of this thread is to debate / compare FToP v. hand ranges, b/c sometimes they argue mutually exclusive actions. (as shown here lolz)