The link you provided was from a site dealing with sub-lets. That particular property does not appear on The Greenwich Multiple Listing Service which shows 6 properties in Greenwich proper offered between $1000 to $1500 a month. The lowest price was $1475 a month.
I would be delighted to speak with you as well but please be careful about any ads that ask for up front or key money.
We have many great rental opportunities in Greenwich. Are you interested in a one or two bedroom? Do you want to be within walking distance to downtown Greenwich and the train station? Of course, your budget will also give me a parameter to search listings for you.