The owner’s insurer can pursue you
If a tenant causes a fire or a flood, the building insurer pays the owner and then seeks to recover that money from whoever caused it. That is subrogation and it is routine. A kitchen fire in a rented house can become a claim against a tenant for an amount they could not possibly pay, and the liability section of a renters policy is what stands in the way.
Shared housing spreads the question
Where several tenants hold separate agreements, one person’s policy does not cover another’s belongings or another’s liability. Each tenant needs their own, and assuming a housemate’s policy extends to you is a common and expensive misunderstanding.
A lease requirement is a floor, not a recommendation
Where a lease demands a minimum liability figure, that number was chosen to protect the owner rather than you. It is a starting point for the conversation, not the answer to it.