Your body adapts to whatever you are doing. If your job involves cutting up vegetables then your mind learns the movements required and over time improves the speed and efficiency with which you can complete the task until it becomes a subconscious level of response. This is discussed in "What is Reality" in reasonable detail and in this interview with a cup stacker.
Part of that learning process when completing a task is that your muscles are also adapting to be good at the task. Fast twitch growth is nurtured if you do lots of "explosive" exercises and slow twitch if you do more aerobic-style exercises like long distance running.
The upshot of all of this is that: Your body will adapt to be better at whatever you are doing the most. If you run all the time, your body will get efficient at running, same for cycling, fishing, weightlifting, swimming etc.
I would be careful with taking fitness facts from anyone who is a "expert", make sure you fact check their comments before taking them as complete truth.
Onto your main question: What does road biking do to improve your running? Road biking predominately develops your leg muscle groups due to the constant resistance of pedalling and will improve your general fitness (reducing resting heart rate, improving muscle endurance etc.) Both of these can help with running. Road biking can improve your understanding of how to push your body and how to manage your fatigue, both of which are important for running.