The first study isn't wrong, nor is your study - one can get "significant" and "nonsignificant" results from the same study. I find the best way to imagine this is to think about the correlation you're researching as having a "True" value and distribution out in the universe, one that - not being omniscient - you cannot know. Each time you conduct a study, you make a single random draw from this distribution, each time getting a slightly better picture of the "True" distribution.
Imagine the True value of your correlation is normally distributed, and centered around 0. If you ran infinitely many studies over and over again, 2.5% of the studies you run will give you statistically significant results that say it's negatively correlated, and 2.5% of the studies you run will give you a statistically significant result that say it's positively correlated. The rest will report zero, negative or positive correlations with p-values ranging from 0.051 all the way up to 1.00.
None of those studies are wrong. They just came from a different part of the distribution - they're different draws, and each new study represents a slightly better picture. That's why repeatability is so important. Some of your evidence says there's a correlation - some of your evidence says there isn't. All you can really say definitively right now is that the evidence doesn't support that there is a correlation, and that more evidence is needed.