Well, most people seem to forget that if you are looking for correlations among N variables, you can't compare each pair with the same standards as if you only had 2 variables. (Remember the recent article about neuroscience papers? Same thing.)
So the damned lie of statistics is pretty subtle, you just have to omit the number of variables you actually looked at when you present your data.
The field of statistics is very concerned with mis-representing data, and has developed a huge array of methods for dealing with uncertainty. It is important for people to appreciate that there are some minimum steps that must be taken for statistical analysis to claim validity. One of the first, which is almost universally ignored in pop-stats like the OP is state your assumptions, then justify them.
Stats are open to interpretation, which is why academia favors peer review, where faulty underlying assumptions can be checked.
So the damned lie of statistics is pretty subtle, you just have to omit the number of variables you actually looked at when you present your data.