Why do properties of colloidal solution depend only on dispersion medium's physical state?
The assumption that properties of colloidal dispersion only depends on the medium is completely incorrect. The vague part of the question is "properties" in the question, because the examiner is not clear about what type of properties he/she is talking about. It is not uncommon to find open ended questions in public exams. The properties of colloidal solutions heavily depend on the temperature (since their viscosity is temperature dependent as well as flow rate dependent). Similarly, the size of colloidal particle controls the optical properties of the dispersion. Similarly the surface charge on the particles determines the sign/magnitude of the zeta potential. If you want to read further, read DLVO theory (named after four persons) on the stability of the colloids from Wikipedia. One should not worry about an incorrect question. If it were a true-false question, one can simply mark it false.