It is in some ways unfortunate that FB uses the word "friends". This, as is evident by the responses in this thread so far, has certain implications. LinkedIn, for example is intended for more professional uses and use the term "contacts" or "connections". I personally think this is better.
That said, like it or not, FB is what people use. I don't like the idea of reading the minituae of peoples lives, but I am very interested to see that since I opened a company facebook page for my company, my website traffic has increased to all time highs - and as a result I am now overloaded with work. So as a marketing tool, it works very well. Friends? Not my thing particulary, and I always only had crap to say about FB.
But times change. How many people remember one saying "why would I need a mobile phone?" for example.
So for FB, I take it for what it is and use it for my needs. Advertising. Marketing.
As for the OP question. In the past if I hadn't accepted a friends request, and subsequently meet them, I simply tell them "we're not friends, we just know or have met each other".
Nowadays, I tend to accept many as the more people I am linked with the more people will know about my business. Free advertising.