Greek hotel caused iPhone 6 damage, how to get reimbursed?

Power went out while charging my phone over night, now the phone nor the charger work at all and hotel says they'll only pay if i get it fixed here. But they don't have an Apple store, so I fear they'd mess with my insurance or do more damage.

How can I get them to either reimburse me, or pay Apple directly?
I'm from the US, have AT&T and do not have Apple Care.

I don't see that happening and I'm surprised they even told you that.

Sorry they didn't cause it, tough luck.

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