From the BBC's iPlayer Mobile FAQ:
Programmes can be played through a
wi-fi connection. Customers with 3 UK
and Vodafone (except for those using
Android, Apple or Symbian 3 devices)
can also access programmes via their
3G network. The BBC is working to make
BBC iPlayer available over more 3G
This seems to hold up with my testing using both the website and the app, I'm on Vodafone UK and get this message on 3G on the website:
Please switch to a wi-fi connection to
play this programme. 3G streaming of
BBC iPlayer programmes is not
currently available for this handset.
And in the app:
Please switch to a Wi-Fi connection to
play this programme.
Presumably the BBC are just checking your connection type and can see it's not a Wifi connection, they're not aware of the reverse tethering you're using and so are just treating it as if its a 3G connection.
Does your company have a Wifi access point you could connect the phone too, that would eb the easiest way to get round this, and I'm presuming if they're happy for you to tether the phone to the PC, then they wouldn't have an issue with employee's devices hooking up to their wifi.