A book came out in August 2024 called "Soda Science: Making the World Safe for Coca-Cola," by Susan Greenhalgh. She's a professor (emeritus) at Harvard. The book is a history. It shows how the Coca-Cola Company turned to "science" when the company was beset by the obesity crisis of the 1990s and health advocates were calling for, among other things, soda taxes. Coca-Cola "mobilized allies in academia to create a soda…
Sure, the raw facts don't care about your feelings, but the way that these facts are interpreted and presented absolutely do care. Two people can look at the exact same data and draw widely different but comparably accurate conclusions out of it.
Using your Coke example, the raw fact that "exercise is good for reducing obesity" is broadly true and not really disputed by anyone as far as I'm aware, but the interpretation of "exercise alone can be a solution to obesity" or "how much exercise vs how much diet restriction is a solution to obesity" is subject to interpretation and biases.