It's total reverse. Low pH prevents Fe3+ from reacting with water to form Fe(OH)3. We can use the solubility product to explain:
Solubility product (sp)=[Fe3+][OH-]3. Sp is only dependent on temperature, and all your experiments occur mostly at room temperature, then Sp remains the same. So at low pH, also low concentration of OH, we will have high concentration of Fe3+. It make possible to determine exactly Fe3+.