It's really rare that a client completely new to you would make an offer like that. Most of the offers you get of that ilk (from Eros) are either timewasters, or outright scams. Or possibly even dangerous.
It's especially common to receive emails like this when you're new. A lot of guys with ill intent will make a sky-high offer in order to entice you... there are a ton of scams in which, say, Mr. So and So is trying to book you during his entire trip to Las Vegas.. wants a companion at dinners and events, etc. Sometimes they even offer more than your posted rate. Sometimes they claim to be famous people.
Also, if you're in NY... there's a notorious rapist who has enticed girls to his home in NJ for overnights. If you don't already have access to a blacklist site, join one.
As for LinkedIn, anybody can create a page there. I even have one for my escort persona... randomly, a company added me to its network, so it's posted that I work there. I wouldn't trust it unless there is information *on the profile* - for example, a published telephone number that's easily searchable and definitely the main number for an established business - through which you can contact the guy, and verify with 100% certainty that he is exactly who he says he is.
When I say 'established business,' I don't mean something that's obviously a template w/little info. Screen the business, too