If you look at the Deed of Trust you will find a provision for FIRE, FLOOD and OTHER HAZARD INSURANCE.  Fairly broad language is  used that allows the lender to determine whether the insurance is adequate to secure their interests in the property.   That provision gives them the right to dictate how large of a deductible they will allow.

Yes they do, however the issue is often as to the maximum amount of deductible they will allow, so the quick way to resolve is to inquire as to their maximum deductible allowable.

As an Insurance Agent (Life), I feel the deductible, should be at  the option of the homeowner.  However the Insurance amount should be the Replacement Value or at least the Mortgage Amount.  I would speak to the Lender's (Manager) to resolve the issue.