Well as far as the BBC are concerned I don't think they're too bothered about losing visitors over screen resolution as the main reasons for visiting their site is the content (the news and weather etc). The fact they like to treat some of their audience badly isn't exactly a new thing when you realize their channels generally broadcast crap like eastenders and they charge us a "tv tax" whether we watch their rubbish or not
From a small business perspective what would be the point in alienating ANY users? One user who could be visiting from a library (known for having shitty old monitors) might have their credit card in their hand ready to buy from you but end up getting annoyed when they have to scroll sideways to read some of your content. When you're running a small business and cashflow is tight you generally can't afford to turn away business because your web designer decided that 14% of your potential web business wasn't worth having.
Sorry I rambled on a bit there!
Cheers,
Robert