As I pointed out in another post, the best interview experience I had was when the guy asked me to bring in my laptop with some code.
I brought in my half finished side project. We talked about it, he asked me some questions, I showed him a couple of things about the tech stack that he didn't know. He asked me to add a basic feature. It worked well for both of us. If I had been faking it I think it would have shown.
I think that's a great approach. I agree absolutely about not being able to fake it either; in practice I've never caught anyone putting forth someone else's code as their own, and I don't think it's a huge concern for the reason you mention.
Do also spare a thought for the people who don't have side projects, or any code that they can legitimately share. There are plenty of talented engineers in that position, and it'd be a shame to have a hiring process that leaves them out in the cold.
I brought in my half finished side project. We talked about it, he asked me some questions, I showed him a couple of things about the tech stack that he didn't know. He asked me to add a basic feature. It worked well for both of us. If I had been faking it I think it would have shown.