Like all words frequently used on the internet, the term ‘based’ is frequently misused. But as for the proper use of the term ‘based’ - that is, when used by men of refinement and nuance - the term really does seem to be a mere recollection of the Aristotelian virtue of μεγαλοψυχία ie. greatness of soul or magnanimity.
Observe Aristotle on the Magnanimous Man:
“he therefore to whom even honour is a small thing will be indifferent to other things as well...
haughty towards men of position and fortune, but courteous towards those of moderate station...
He will not compete for the common objects of ambition...will be idle and slow to act, except when pursuing some high honour or achievement...will not engage in many undertakings, but only in such as are important and distinguished.
He must be open both in love and in hate...care more for the truth than for what people will think...does not bear a grudge...is no gossip...is not given to speaking evil, even of his enemies, except when he deliberately intends to give offence...
Other traits generally attributed to the great-souled man are a slow gait, a deep voice, and a deliberate utterance; to speak in shrill tones and walk fast denotes an excitable and nervous temperament, which does not belong to one who cares for few things and thinks nothing great.”
Nic. Eth. IV.III