He's having fun with the expression.
In another context it can be used sarcastically to imply that the person does care while denying it, as Mitchell says, but that's not so in all contexts and certainly not true in my usage. While the phrase literally says one thing (that it would be possible to care less because the person does care to some degree), in common usage, with the 'not' missing that's not the meaning but it actually depends on context.
It's a subtle thing but my "could care less" phrase is used in this case to mean "could not care less" and I am unapologetic about it because the exact meaning can be nuanced according to context (and clever contextual wordplay).
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