Is there a way to configure the robots.txt so that the site accepts visits ONLY from Google, Yahoo! and MSN spiders?
There are more than 3 major search engines depending on which country you are talking. Facebook seem to be doing a good job listing only legitimate ones: https://facebook.com/robots.txt
So your robots.txt can be something like:
User-agent: Applebot
Allow: /
User-agent: baiduspider
Allow: /
User-agent: Bingbot
Allow: /
User-agent: Facebot
Allow: /
User-agent: Googlebot
Allow: /
User-agent: msnbot
Allow: /
User-agent: Naverbot
Allow: /
User-agent: seznambot
Allow: /
User-agent: Slurp
Allow: /
User-agent: teoma
Allow: /
User-agent: Twitterbot
Allow: /
User-agent: Yandex
Allow: /
User-agent: Yeti
Allow: /
User-agent: *
Disallow: /