I did see a few screen scrapers. However, that isn't really necessary. They provide a nice computer-readable data file once you are logged in. It is a simple JSON page. It shouldn't put too much load on their servers.
However, your point is taken on relying on (another) third party.
Has anybody explored spoofing the DNS so the bridge talks directly to your server? That might avoid having to go into promiscuous mode. Although, spoofing DNS comes with its own hassles.
Famous last words.
Some spoof the DNS. There are various other ways people have done it depending on their particular skill set, experience, and what they have available.
The way I do through the Pi is set up a bridge between two network ports and let the traffic flow through it. That way you don't have spoof anything or deal with promiscuous mode.
Some others run OpenWRT on their router and mirror the data to another machine.
Many use Meteobridge if they want a commercial solution. Or Kevin Key's Windows software.