If this happened in a property you owned, the fire department would kick down the door anyway. This is no different. Why would a landlord even know your property is on fire before the fire department kicked the door down? Emergency services would be there long before the landlord even knew anything was amiss... and there's a high statistical probability that it was me that called emergency services in the first place and the door would be unlocked. I'm not calling my landlord first, shit needs to be dealt with now, not when the landlord finally checks their voicemail.

So this argument makes little sense to me.

And as another commenter notes - that's what renter's insurance is for.