When you word it like that, the standards are a lot higher than "seem very intelligent", or at least narrower- you need to know their track record on decisions like this.

You don't need any specific kind of proof, you already have some state of knowledge about correctness of such statements. There is no "standard of evidence" for forming a state of knowledge, it just may be that without the evidence that meets that "standard" you don't expect to reach some level of certainty, or some level of stability of your state of knowledge (i.e. low expectation of changing your mind).