It's sad to hear that anyone died that way.
Sometimes people get strong suicidal impulses from a quirk in brain chemistry, that might otherwise have corrected itself relatively quickly and without any treatment at all. Or to put it in real language -- sometimes there just isn't any good reason.
There are an enormous number of good reasons why a suit (almost certainly) could not succeed against Fox, Ramsay or anyone else associated with Kitchen Nightmares. Even if Ramsay and/or the show actually was part of his misery, it would (again, almost certainly) be frivolous to the point of severe sanctions to even bring it.
Not that it signifies particluarly, but there are reasons troubled restaurants line up to get on Kitchen Nightmares (now casting!). Did you know that if your restaurant is chosen for an episode of Kitchen Nightmares, you get a remodeled kitchen and redecorated FOH as part of the deal? Not to mention Ramsay's recipes/menu, his truly sound business advice, and the continuing resulting publicity.
Yes, Ramsay can not only trash-talk like an ex- athelete, he can find and push emotional buttons with the impact of an angry spouse. But, if you don't know in advance that Ramsay in your kitchen isn't a walk on the beach, they'll explain it to you before you sign the contract (absolving them of liability).
BDL