tenant wants language in lease to make landlord liable

[Sid Langley]

I'm just starting to rent my house out.  I selected a tenant with an excellent background check.  I presented her my rental agreement, which says in part:

"All personal property on premises shall be and remain at tenant's sole risk, and owner shall not be liable for any damage to or loss of such personal property arising from any cause whatsoever. Tenant understands that it is advisable to obtain personal property and premises liability renter's insurance from a provider of tenant's choice."

She refused to sign, and proposed instead that it should say:

"All personal property on premises shall be and remain at tenant's sole risk, and owner shall not be liable for any damage to or loss of such personal property unless caused by the owner's negligence.  Owner is liable for damages or injury to tenant or guests if caused by owner's negligence.  If owner fails to repair a problem after being notified by the tenant, owner assumes liability for resulting damages."

Is the tenant's request reasonable?  It seems to leave important things out, like allowing a reasonable time for owner to perform repairs after tenant's notification.  But even if the wording is improved to cover that, is it reasonable?  Though I hope it never happens, what if some accident like a burst pipe happens to damage the tenant's property and it's later determined to be something the owner was responsible for (but the owner was not grossly negligent).  With a typical, well-written rental agreement, would the owner be liable for the tenant's property damages in such a situation?

Thanks.