A worker employed by subcontractor R.A. Robinson was in a car accident while traveling to a job site. The injured third party (Woodring) tried to sue the general contractor (KGP) and the main client (AT&T) based on insurance requirements in the subcontract. The court ruled that insurance clauses in subcontracts protect only the contracting parties—not the general public—so injured third parties cannot use those clauses to sue the general contractor or client.
Insurance requirements in your subcontracts protect your client and the general contractor, not members of the public injured by your work. Third parties cannot sue based on those insurance clauses.
Maintain the insurance limits your contracts require (here: $1M per accident for auto liability). This protects you from direct claims, even if third parties cannot use the contract clause itself.