The use of parametric insurance is promising as its payouts can be directly tied to hazard indicators and thus provide a fast-tracked claim-to-payout process, which improves liquidity in times of disaster. In parametric insurance, policies are determined by a loss threshold (modelled or sustained) or physical hazard severity (e.g., rainfall or wind speed). In the latter, when the severity of the hazard exceeds a threshold, a payout is automatically triggered according to the insurance contract terms to compensate the policyholder without needing a loss assessment. Recently, blockchains have been proposed to improve the efficiency of insurance product offerings (e.g., to cut administrative costs associated with the premium collection and claim processing) and to efficiently store and maintain information (e.g., immutable distributed storage for audits). While parametric insurance would certainly benefit from these blockchain implementations, existing proposals mostly depend on a single source of truth for payout calculations. In this paper, we present a novel trust-based framework to handle multiple sources of truth in parametric insurance products which use blockchain technology. This framework alleviates the reliance on a single point of failure (either through accidents or malicious abuses) and outperforms its statistical counterparts. We discuss how parametric insurance would work under such a framework using real-world use-case scenarios, show the use of subjective logic to reason about multiple sources of truth, present the architecture of the framework, and examine a detailed blockchain-based implementation using an Ethereum private blockchain. Our results show the feasibility of the proposed system in practice.