I frequently wonder - is Facebook allowed to say, "bing, you can crawl us. NewCompetitor, you cannot."

I feel like once a company allows public access by posting stuff on the web, they can specify terms, but not include/exclude groups specifically. (In a legal sense; I understand blocking systems that hammer servers but will respect robots.txt. IME bing is the worst offender -- they hammer my sites, send no traffic, but will stop if I specify in robots.txt.)

Does anyone have an opinion about "once public, I can crawl"?