No one is saying that. A cancelled power or ability returns at the end of your turn.

So clearly, I got caught on another piece of Jargon.

The canceled vs countered bit is something I didn't get.

So for specificity:

I can cancel any power/ability I possess. That means it's still on my dial, I still possess it, but I am not using it. It lasts until the next player goes. This distinction primarily refers to Stealth, as it is the only power that would need to be canceled rather that not used. (I'm sure there are some special powers that this might apply to as well, but I couldn't find another colored power that I would want to do this to)

Any countered powers are done by another player/game effect and they last until the beginning of my next turn. This is your typical outwit, special power or game effect done by another player.

Any power that says I may use, I can turn on and off as often as I like in a turn, before or after any action, but not DURING and action.

Is that correct?

The current wording allows you to be using BCF while still allowing you the option of choosing to roll or not.
"Blades/Claws/Fangs
When this character is given a close combat action, you may roll a d6 after making a successful attack roll. The result replaces this character’s damage value, then that damage value is locked until the attack resolves."

The duration of countering can depend on the circumstances by which the power was countered. In general, the power is countered until the beginning of the Outwitter's turn.

You can only cancel at the beginning of an action, not after or during.

And the same applies to using/not using. It is assumed you are using a "passive" power (a power that does not require an action to use) unless you indicate you are not using it at the beginning of an action. The beginning of the action is also when you would indicate you are not using a power, not after or during.

Since this is the second time I've seen you mention this recently, I assume you are firmly in the camp that you can indicate you are using BCF, but then choose not to roll it after the successful attack roll. (This is a good way to mess with an opponent's PC.)

I'm asking in large part because if this is the ruling, then it is a big change in the rules that I don't think many people are aware of. (nbperp actually used Flurry and BCF as an example of not being able to do it shortly after the 2010 Core Rulebook went into effect.) I'm also asking because I PMed the question to nbperp back in December and he never responded.