As a renter if it was my incompetence/negligence that caused it I would take responsibility and replace it.....
Keeps you in the landlords good books so they don't start looking for excuses to replace you.
I'd think it's the other way around personally.
Landlords are wanting to keep good tenants. The OP even says that he thinks they're generally good tenants (aside from this fire and a bit of general untidieness).
When we used to rent, we had an issue wehre the kitchen floor tiles started cracking and coming away from the floor underneath. I think it was a mix of damp coming through the walls and our washing machine leaking. The landlord was exceptionally good and had no problem with replacing it, even if they did know it was partially due to our washing machine.
In return, I believe we were very good tenants, we always paid our rent on time and maintained the gardens, shed, fencing, etc pretty well.
If they hadn't replaced the floor, we would have paid for the floor and then given our notice to move in straight away, there was certainly no shortage of houses to rent near by. The house would have then stayed vacant for a while whilst they found a new tenant.
If I was a landlord, I'd be wanting to keep what I consider a good tenant for the sake of a £200 oven.