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Reliably sourcing statements is the act of finding reliable evidence to support contentious statements in articles.

An aside in a minor article in a high-quality source may be no more 'reliable' in reality than the front page headline in a tabloid. All sources can get things wrong, and everything taken from a source needs to be looked at on its merits. This is (in theory at least) what existing policy requires, but we still have endless debates over arguments that 'statement X is from reliable source Y, so we can include it in article Z'.

As Reliable Sourcing policy notes (at section WP:NEWSORG):

Whether a specific news story is reliable for a specific fact or statement in a Wikipedia article will be assessed on a case by case basis.