It's not a Fight action, but it's a close combat attack. And any close combat attack follows all steps described p68-69 of the rulebook, just like any ranged attack follows those described p64-65 of the rulebook.So your argument to not allow TGB is because it doesn't say "a Shoot action", yet you want it to be a full Fight action despite the fact that it does not say "a Fight action." That doesn't persuade me.
A ranged attack can happen for a number of reasons, the most common being a fighter performing a Shoot action (but it can also happen on a Fire through ductway action, a Blind fire action, or as a result of this Tactic card, for instance) just like a close combat attack can happen for multiple reasons, the most common being a fighter performing a Fight attack. I'm pretty much paraphrasing the first paragraph from page 64/68 here.
TGB (p67) is a special rule that specifically can only be used when making a Shoot action, not any ranged attack. Determining attack dice, on the other hand, is a regular step of the close combat attack process and not something tied to the Fight action.
And, according to the rules, pulling the trigger of an Unwieldy ranged weapon takes twice as much time as multiple CC strikes. That a mortally wounded fighter can lift their lascannon and shoot that guy at the other end of the battlefield with no penalty whatsoever bothers me just as much as them going all Kenshiro on their killer.