They are looking for proof above a certain probability level, typically p>95%. If they don’t find it that doesn’t mean there is no link. It just means that they can’t say for 95% sure that there IS a link.

There could be a whole lot of reasons for that, other than there being no link, and I explained what some of those might be in my prior post.

Also, if the study comes back with p>80% that means no link will be the conclusion even though there is an 80% chance the result was not by chance.