There is an explosion in applications that are essentially one website browsers. They talk to Netflix, Twitter or what have you via an API that can be anything from HTML screen scraping to SOAP and REST web services.
I think it would be a pain to have to have two websites to ask Twitter questions, one for those using MSIE, Firefox, Chrome, etc and one for TweetDeck, and other clients. Worse, things like browser plug-ins, Java applets, flash clients all kind of fall into a middle ground.
Worst of all, unless we give an IT IQ test to people asking questions, we are expecting them to know a lot about the inner workings of tools like browsers that use Twitter or tools like TweetDeck that also use Twitter, but use OS specific libraries and web APIs.
And what about Flock, those super browsers? If I use Twitter through that, I honestly couldn't say if it is a custom client or a web browser.