That's actually a good point
But still, how do we know that you're not desperate to defend yourself and lie? How do we know that you weren't investigated and you are now ready to start a "my word against your word" with the real detective? The detective maybe isn't here right now but he/she will be later.
That's in case you're lying....but now I think that you might be telling the truth

It would be too much if the same trick works twice in a row. Especially not by a good player like you.
You fucked my brain, fuck off