Yea, and that is because these videos are concept videos that aren't canon. It does not have a deeper meaning.
You know what else is there that isn't in BBS?
Terra gets a Thundaga to the face when Vanitas jumps from the mountain, Ventus' Keyblade shatters when he is frozen and thrown of from the cliff, Terra's arm gets frozen by an attack from Xehanort and Ventus is also left-handed.
These are all things that are not in BBS itself as well.
The simplest explanation is that by the time the video in KH 2 FM was made, Nomura simply had not yet designed the Keychains for TAV's keyblades.
It's the same as to why TAV's faces weren't shown in the secret video in the original KH 2: Because Nomura did not have their faces completely designed yet.