And the coyotes do? Come on.
Their job is to move as many people over the border as possible; they're going to do and say anything to make that happen.

So what? They don't need to get them to lie about anything to make that happen. Again, the coyote's job stops at the border. Once the people cross (or are taken across), the coyote's done with them. They don't care whether those folks get to stay in the country.

They'll tell them what they should do when they cross ("Find the CPB and tell them you want to apply for asylum") so that these folks aren't just sitting there. But they're not creating some fictional "legend" for them to memorize for their hours-long credible fear interview. These guys do transport, not immigration services.

You don't just get to stay in the country if you say the right three or four phrases when being picked up. You're going to get interviewed about where you're from, what happened to you there, why you left, and what would happen if you went back. So no coyote is going to be writing them a script. At most, they'll be giving them the basic advice - talk about what you were afraid of back home, anyone in your family that was hurt or imprisoned or killed because of who they were, any threats you received, etc.