Correlation doesn't imply causation: it just provides evidence that there may be a link between two variables.
The process of getting more evidence for specific causation involves getting more data and assessing whether there is evidence for a more specific kind of causal connection between a bunch of variables.
The underlying reason why we can't say there is an implication is because we can't assume complete information: this is the real heart of the argument. If we had complete information then it would be another story but we don't.
In the end though, you have to make up your mind and this is regardless of the correlation value, the data, the analysis and the conclusions but the best thing is to make these decisions with the best kind of information available and this is what statisticians try and do for their clients: they try and give the best advice they can but ultimately they don't make the decisions: the people who are the decision makers make the decisions.
In terms of the parents worrying, this will come down to how important the think the issue is for them to take the necessary action just like any decision maker: if the parents consider it important enough then they will make the decision to investigate it further and take further action but they may not care to not take any action at all or even believe that the results and the analyses are even real: in order to go further you need to consider that something is important in order to go further.