co-ops can refuse you for any and all reasons with no legal consequence.
my family owned a home in silver beach many years ago. the home was sold to pay the nursing home for my grandmother who was the owner. I was not in any position to try to buy it myself but it certainly would have been interesting trying to find any residents who even remembered my grandmother and would sign a letter for me.
A child of an owner within silver beach was the buyer. There is no doubt that our family didn't get the best price. It's not an open market compared to other resales though it really didn't matter. My grandmother outlived the proceeds in the nursing home.
The advice to look elsewhere is good advice barring great fortitude and a bottomless bank account to take on these kind of exclusionary practices legally that pursing in the current legal environment is a real crap shoot as to whether you will prevail. Remember that in Manhattan, a much pricier environ, movie stars and rock stars routinely get rejected by co-op boards with no recourse. The court's always side with the co-op. Co-ops and condo associations are a form of government and are essentially sovereign as to what happens within their borders (whether its a building or a community like Silver Beach.