This is very common lab for second semester general chemistry in the US. The purpose of the lab is for the student to come to the conclusion that Borek did. If done correctly the student ends up with a molar mass that is then divided by the one given in the periodic table (32 g/mol) and S8 is obtained. However, for your results 93/32 you end up with S3. As your instructor/professor said, sometimes, it does not work as expected.
For this experimnet, graphing of data and correct extrapolation is crucial. Also, this experiment, typically has two parts, where the first part has the student calculate the freezing points constant (Kf) of naphthalene first. This value is used in part two of the calculations to find the molar mass of the solute (sulfur in this case) If Kf is calculated incorrectly then the molar mass of sulfur would also be incorrect.
Students are usually taught abou the diatomic elements, H2, O2, N2, etc, in this experiment they find that other elements such as sulfur and phosphorus are not monoatomic in the free state.
Thus the student should arrives at the question/answer that Borek is proposing. You can see James F. Hall Experimental Chemistry 6th edition for a description of this lab.