I believe the deductible only applies to the property coverage and not the liability or medical payments coverages.
Out of curiosity I called our renter's insurance carrier and asked them what it would cost to increase our medical payments from $1,000 to $5,000 (their maximum for med pay). They said it would make no difference to the minimum premium we currently pay, so I asked them to increase the med pay limit. I think the cost to increase med pay would be pretty modest even if it didn't fall within the policy minimum.
Many wealthy people are little more than janitors of their possessions.
Frank Lloyd Wright, architect (1867-1959)