Good morning Jim,
In NY the home inspection is done PRIOR to signing a contract NOT the reverse so that gives the seller time to change his mind or accept a higher offer, as well as the buyer can also change his mind and walk away; it works both ways.
There's NOTHING in writing other than a written offer which we call the Sales Agreement or more commonly called The Offer. The Sales Agreement/Offer is signed by the buyerwhen presenting an offer but very rarely signed by the seller. This would have given Tony more of a leg to stand on as it's actually legally binding but sellers DON'T typically sign the other half of Sales Agreement/offer and you can't force them; this is how it's been for years now - common practice.
So with that there is NO legally binding contract until a returned signed copy, with the sellers signature included, is sent to the buyers attorney; this is what we call a fully executed contract. Tony didn't have a fully executed contract in place so despite the other out of state advice he doesn't have a leg to stand on. Maybe, just maybe out of courtesy the seller can reimburse Tony for the home inspection, he can ask his attorney to help with that but it doesn't always happen. The best thing for Tony to do is move on and find another house with the knowledge of knowing that this could happen.
Not the best system, but it is what it is, I hope that's a little clearer. Have a productive day.