'Freesat iPlayer uses press red to start then broadband to stream
The service uses a variation in the "Press Red" function of the satelite stream to initiate the internet connection to the iPlayer servers. All the video downloading is using the ethernet port - as you say using your current broadband.
The crucial difference for owners of Freesat TVs is that you don't need an extra box to view iPlayer. So now you get subscription free HD broadcasts (Freesat) and also subscription free video on demand (iPlayer).
The ethernet port is mandated as part of the specification for Freesat devices. The important factor for the BBC (et al) is that the capabilities of the viewing devices are known and standardised so one implementation by the broadcaster should work for all Freesat branded devices - at least that's what we've been told. I'll only know when Panasonic update my plasma.