Telepathy Band allows you to use another Rocketeer's Overkill Option. From who's perspective is the power used? We went with the Rocketeer with the Power, not the Rocketeer with the Telepathy Band.
I'm afraid you've got it reversed. The Rocketeer wearing the Telepathy Band can use the Overkill Option of a different Rocketeer.
Example 1: DeSoto has the Telepathy Band and uses the Captain's Command option. The Captain can't get a Command AP and DeSoto can, right? It's as if the Captain is using the power not DeSoto. So the Captain has to give the extra AP to someone in his own square if he doesn't have the Tele-Radio (even though this is happening via DeSoto with the Telepathy Band).
In the above example, if DeSoto achieved an Overkill, he would be able to assign a Command AP (including giving one to the Captain). It's as if the Captain's Overkill Option text were temporarily written on the Chief's character sheet.
Example 2: The Captain has the Telepathy Band and uses DeSoto's Strafe. The extra hit is on an alien in range/LOS of DeSoto, right? Even if he's on the other side of the map from the Captain?
If the Captain rolls a few Overkills, he can spend a charge on his Telepathy Band, and spend those Overkills Strafing aliens in range and LOS of a weapon he's using.
So basically, the Rocketeer with the Telepathy Band isn't "borrowing" the power, they are actually transferring an Overkill Action to another Rocketeer.
Afraid not -- it's the Rocketeer with the Telepathy Band that is basically borrowing the power.