Oh come on. They violate reality with that many ninjas overcoming the single old ninja! That's how you know it's a put-on!
Clearly, Matt and Izo worked out ahead of time that Matt would piss and moan, Izo would be unhelpful and Matt would say sorry that RIGHTEOUSNESS demands his sacrifice, but it's all for the best..The Hand's history is full of people claiming that they'd infiltrate them and destroy them with Justice. They're EXPECTING THIS. Izo knows them well enough to know this, and so does Matt from Elektra.
Izo is a nearly immortal martial artist; stopping his heart and breathing so he can fake being dead is nothing. The Hand sees what they expect to. They don't really know Matt, how stubborn he is and how devious.