Not disagreeing, just extending. Dark Sky merges multiple weather data sources, even in a single country, and I use it for a private app that deals with weather all around the world. An open source project could just be code, not a service, but that code should have a config where you specified which sources to fetch and how often instead of choosing "a given govt-funded weather source".
Of course, if it's designed to be extensible then definitely non-public sources could be added, but whether they'd be supplied as included modules/plugins or need to be developed (and then optionally contributed upstream) by users of a given non-public service is a question of practicality and sometimes cost (if it's a paid service an OSS project may not be able to justify the cost of a licence/account for the service to develop/test against).
