The falicy is that bikes are prohibited from riding on footpaths with very limted exceptions.
From NSW Government Road Rules for bicyle riders:
Riding on a footpath
Generally, bicycle riders must not ride on a footpath. However, children under the age of 16 years can ride on the footpath unless there is a NO BICYCLES sign.
Bicycle riders aged 16 years and over must not ride on a footpath unless they are:
- an adult supervising a child under the age of 16
- accompanying a child under the age of 16 where all children are under the supervision of an adult
- a postal worker riding a bicycle in the course of their work duties
- a rider carrying a child under 10 as a passenger
- a rider with a medical condition who is carrying a medical certificate that states a medical practitioner believes the rider should be allowed to ride on the footpath
- a rider accompanying a rider with a medical condition.
They are alos prohibited from riding on pedestrian crossings and must dismount.