Who ‘Owns’ Consequence Invocations?

For a while, I assumed that all Free Invocations, just like FP-powered Invocations, are ‘owned’ by players and GMs (not characters), and can always be passed around at will to benefit another character so long as it makes sense based on what’s happening in the game world (Condensed page 19):

A free invoke, as the name suggests, lets you invoke an aspect without spending a fate point. You can even let your allies use free invokes you have created.

However, yesterday after a game, a player pointed out that the text about Consequences (on Condensed page 36) uses a different wording:

And, just like the aspects you make when you create an advantage, the character that created the consequence—that is, whoever shot you—gets one free invoke on that consequence.

(Bolding mine.)

So does that override the default assumption that invocations are ‘owned’ on a meta level and can be passed around by the players in whatever way makes sense, or does the player of said character retain the usual freedom to transfer the invocations?

The distinction becomes relevant for at least two situations:

  • When another character in the same Conflict could benefit from the invocation in question. Whether the character (not player) who inflicted the Consequence needs to do something to pass over the invocation (and even can do so at all) makes a major tactical difference.
  • When the initial successful attacker perished in the Conflict. If the Invocation is tied to the character (not player), then presumably it expires with the character, thus being much less of a concern for the opposing side.

Also, if this one of the small differences between the different implementation variants of the system (Condensed, Core, FAE etc.), I would like to know. (Current campaign is using Condensed and I’m trying to avoid dragging in stuff from other implementations in order to keep things clear and simple for everyone.)