Am I interpreting this correctly in thinking that he wants to show that there is no correlation between the variables? I think he really needs to know that not finding a statistically significant correlation is NOT evidence that no correlation exists. It merely indicates that one has not managed to find evidence to reject a null hypothesis of no correlation (and we are unlikely to find such evidence with such a small sample).

Trying to make a claim that no correlation exists because a correlation coefficient calculated with a sample size of 9 is not statistically significant is nonsensical; I agree that this is inappropriate. More formally, the problem is inadequate statistical power. Using this calculator, we can see that even if the true population correlation between the two variables is 0.5 (a quite strong relationship in the social sciences), the probability of observing a statistically significant relationship at the .05 alpha level with a sample size of 9 is just 29.5%!! He needs to perform statistical power analysis, decide on a more appropriate sample size, and get more data.

Another issue is that his datapoints are unlikely to be independent, given that 3 of each come from the same company. Independence problems and other possible issues are quite hard to judge given that we don't know much about the project/data, though.