You're just being pedantic. That's not helpful. Obviously the point here was about "credulity", not proof. The very existence of a replication crisis in statistical science like this is an existence proof of what I meant. You don't just take papers like this at face value. You can't. They're simply wrong too often.

In the kind of first principles sense you are thinking of, sure, proof is proof. But in the real world the burden of proof for an epidemiological headline like this absolutely is much higher, in the practical sense of "should I believe this bullshit or is there a mistake somewhere?"