I'm not an expert but is that true? Road bridges are commonly concrete. In this application they use tensioned steel inside the concrete to help with the tension and other forces.

Yeah exactly. The steel resists the tensile forces and the concrete resists the compressive forces.

Concrete is very weak in tension. That's why it's basically never used without steel reinforcement. I think increasing the tensile strength is mainly useful to prevent cracking which looks bad and can allow water to get to the steel.