The owner is named even when the tenant was responsible
A drowning or serious injury claim typically names the property owner alongside the occupant. Whether you were present, and whether the tenant invited the person, is argued afterwards. The liability limit on the landlord policy is what stands there while that happens.
Barrier requirements are a legal condition, not advice
Arizona imposes pool enclosure requirements on residential property. A non-compliant barrier is evidence in a claim and can affect both liability and insurability. On a rental the owner cannot verify the gate daily, which is why the condition of the fixed barrier matters so much.
Some carriers restrict pools on rentals specifically
Diving boards, slides and unfenced pools narrow the market, and a few carriers decline rental property with a pool at all. It is an underwriting question to settle before buying a property, not at the first renewal.