I think that rule already applies to any uncontrolled character in the rules as written. That just means that the scenario in my initial message stands as it is, regardless of whether the transporter chief is a Supporting Character or a Main Character.
But I was inspired by the discussion on the use of Traits in Supporting character weapon damage seems irrelevant - #14 by aramis to come up with the following solution:
Again, the away team needs a site-to-site transport into a vault, and also out of it. The Task is Difficulty 3, so an uncontrolled character can’t do it. That just means that we need to apply enough Advantages to reduce the Difficulty to 0.
The most obvious thing is that the commanding officer in the away team gives instructions to the transporter chief, which is a Create Advantage Task using Presence + Command at Difficulty 2. If they succeed particularly well (this should be the commanding officer’s area of expertise!) they can spend two Momentum to create a double Advantage. If the roll fails, the GM can suggest Success at a Cost, and take two Threat to raise the stakes. Maybe the characters hear some noise, indicating a Klingon patrol nearby?
But there is probably still some Difficulty left on the transporters Task. The next most obvious thing to do would be to introduce another Supporting Character, perhaps stationed at Ops, coordinating with the away team. An uncontrolled character can be used as an Advantage.
Now there may still be one Difficulty left. Perhaps the transporter chief is having trouble locking onto an open space in the destination area, and they need an away team member to scan the area with a tricorder, performing a Control + Science Task at Difficulty 2 to create the final Advantage needed. Again we may apply Success at a Cost if the roll fails. This time it might be appropriate to take the Threat and spend it, having that Klingon patrol discover the away team.
Does this seem like too much business to impose on the players? Maybe, if all that is needed is one quick transport. But in that case we can always fall back on the Direct Task, possibly ending the scene as all of the player-controlled characters are beamed out of the area.
But in a more complex scenario, where multiple uses of the transporter are needed within the same scene, using Advantages seems like the right call, because once those Advantages are in place, the Difficulty of the transporter task stays at 0 for the rest of the scene. The effort the players put into it initially is rewarded with the ability to transport at will for the rest of the scene. That sounds pretty cool.