I don't see the Jets being too enthusiastic about dealing with him and his agents.
Joyner is on a cheap one year deal, so I wouldn't think that he would actually be prohibitive for taking Hamilton. If he and Davis are competing for a spot and he loses out he could very easily be cut during TC.
You would think between Joyner, a guy they targeted as the starter last year, and Davis, a former 3rd-round pick under Douglas who started a lot last year, that they would think they have their 2 primary safeties. But again, they might view Hamilton as that unicorn.