Assuming they did not adjust their p-values for the multiple comparisons, this result will not be valid. Of course, the issue here is that the researcher did many comparisons and reported the top hit. "is there a quadratic relation between these two variables?") and so on until they finally find a "statistical significant" relation. After coming up negative, they "recast their net" with a different question (i.e. "is there a linear relation between these two variables in our data?"). In terms of statistical analysis, "a fishing expedition" just about always has a negative connotation the idea being that the researchers started with one question about their data (i.e. However, I try to point out what I believe to be the differences. There is plenty of overlap between these two concepts, so there is not a clear distinction.
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