I 100% share your cynicism with regard to this world.
Yet I am speaking from experience.
Here's how it went down last time:
"Yeah, so, I dropped it in the sink. I have this paperwork from the Apple store."
"Wow, okay. I'll start the claim for you. Someone will give you a call in a few days."
A few days pass. I get the call.
"You dropped it in the sink?"
"Yeah, right into the one bowl in there full of water."
"Okay. What did you pay for the replacement? Oh, I see it on the paperwork here. Okay, thanks."
A few more days passed. Then I had a check in my mailbox.
It helps, I think, that I'm going through a real, consumer-facing insurance company instead of an outfit that sells coverage through a retail middleman. Retail extended warranties are, indeed, bullshit, but the distinction here is that I'm buying real insurance, which covers accidents and liquid damage.
They also cover my car, my apartment, and a life policy I have to pay off my student loans in case I should meet an untimely end.
But they're the real deal and they haven't screwed me yet. I suspect if I made a regular habit of making claims on my policies, it'd be a different story. So far, though, it's all good.