The sample size has nothing to do with the distinction between a survey and a study, as far as I know. Either could have a small sample size or a large sample

The sample size has nothing to do with the distinction between a survey and a study, as far as I know. Either could have a small sample size or a large sample size. If they got a statistically significant result given some alpha value, then that's a valid result, assuming the experiment itself was set up in a valid way (random sampling, controlled, double blind, etc.). Statistical significance tests take the sample size into account. A large enough difference can make up for a small sample size, and vice versa.