Pretty much that. You can still be "on" and logical without giving a fuck. All of my favorite people could be described as being both "on" and "off."

If I weren't worried he suspects me of "chemically poisoning" him ("I've got all the symptoms" - doesn't know which chemical, but he's insisting someone poisoned him), my favorite person would be a completely cuckoo bananas, drug-addled co-worker who once came out of the bathroom and asked, "did you just feel the momentum shift?" "What the fuck are you talking about?" "I just shifted the momentum and was wondering if you felt it." There's someone who doesn't give half a fuck about anything, but he still cares about some things.

I think the transition from "not caring" to "not giving a fuck" (and there IS a difference!) is probably the most difficult phase in growing up, one many people never go through, and the transition probably most important in becoming a character. Trolling is maybe the most effective method of converting GaFs to DGaFs... following through and never revealing to the victim you really didn't give half a fuck when you insisted "you still need to file a near-miss report for OSHA compliance because you already plugged those powered speakers into a non-GFCI outlet."