Well,

Can you tractor beam a ship off the board?

Since it isn't addressed, I'm going to say, no you cannot.

The part of the FAQ stating that you cannot boost or roll (or decloak) off the board never refers to them as actions. Just as boosts, barrel rolls and decloaks.

So as the Tractor Beam card does not allow you to do it (like it does with obstacles), you cannot beam someone off the board. They are still performing a boost or roll, action or not.

There seems to be no suggestion that you can break that part of the boost and barrel roll rules so it certainly isn't allowed as written.

Note that there is a specific allowance for obstacles but this has nothing to do with the board edge.