This is not true in California. I had a landlord who wanted to enter all apartments to inspect for evidence of pets (someone had seen a cat inside the building) and I told them exactly where they could shove it.

(Paraphrased from CA Civ Code 1954)

A landlord may enter the dwelling unit only in the following cases:

- In case of emergency.

- To make necessary or agreed repairs, exhibit the property, or perform move in/out inspections.

- When the tenant has abandoned or surrendered the premises.

- Pursuant to court order.

If I were your landlord and you refused, I would sue for violating a no-pets clause in the lease to get a court order to allow the inspection. Or perhaps just initiate eviction proceedings for the lease violation.

It is what it is.