Bucky's instincts tell him this might be an honest cop -- and as he looks more, he suspects this man might have been one of the mutants killed during the Sentinel Revolt which took the life of Xavier, back in his homeworld. Men close to Xavier generally had their heart in the right place... even if some of the survivors eventually went to Maestro.

But still, he's a cop. He's not going to want to hear fantastic stories of extradimensional travelers going around Quantum-Leaping everything right.

As they settle in, Bucky asks, "Why don't we start with what you know?"

If he's going to come up with a convincing lie, he needs to know the story of what happened to him in this world.

Since this guy likely won't believe the truth.