My text book (*Fundamentals of Physics* by Halliday et al.) mentions the following about the work done in internal energy transfers: 

> An initially stationary ice-skater pushes away from a railing and then
> slides over the ice. Her kinetic energy increases
> because of an external force F on her from the rail. However, that
> force does not transfer energy from the rail to her. Thus, the force
> does no work on her. Rather, her kinetic energy increases as a result
> of internal transfers from the biochemical energy in her muscles.


This is confusing me a lot. The energy transfer is clearly internal but work must be done by the force as work done is **defined** as the (dot) product of force and displacement and the definition makes no reference to any transfer of energy. 

I thought work done by a force just means that the force is Causing a transfer of energy To (or from) an object, and gives no information about whether the energy js coming from the object exerting the force.

**Edit:** 
My confusion is not over whether work is being done or not but which force is doing the work which ends up causing the change in kinetic energy