This pattern is used to frame a statement as someone else's opinion or as a hypothetical judgment. It often appears with people, organizations, or types of people (e.g., 医者, 母, 彼). The phrase implies 'if you were to ask them, they would say...' and can carry a nuance of emphasis or contrast with other views. It is somewhat formal and more common in written or spoken argumentation than everyday chat. The subject of the opinion is marked by に, and the following clause gives their typical or likely response. Note that the expression can also be used with a general 'one' (e.g., 私に言わせれば meaning 'if you ask me'), but it's not limited to first person.