Every language in every society has its own colloquial shorthand. It's a kind of mental shorthand we all learn.

The phrase "on record" is colloquial shorthand for the context of records from direct human observation. The colloquial shorthand informs us intuitively that any other kind of record is NOT by direct observation and therefore needs qualifiers to denote that.

In the English language, there is a broad colloquial shorthand we all rely upon. "On record" is one of those bits of colloquial shorthand. Logically, you know this but are nitpicking an esoteric point of language use to dismiss the very basis of climate change reporting.