This is not an ambiguous phrasing; this is a standard way of writing the summary in prose. There is nothing remotely “suspicious” or “malevolent” here.

It clearly expresses that the only one of four categories whose callback rate rises to the level of statistical significance (presumably something like p < 0.05 of null hypothesis that all rates are the same) was the rate for high-class men. The reason the sentence doesn’t include the word “statistically” in the second half is that it would sound incredibly awkward, and is not necessary to repeat.