No. The Schengen treaty affects (maybe not that strictly) visa policies for the member states in the way that all the members are expected to have the same visa

No. The Schengen treaty affects (maybe not that strictly) visa policies for the member states in the way that all the members are expected to have the same visa requirements (that's quite logical). There are only some old EU15 members listed, but not a single country from the 2004 extension, nor Bulgaria and Romania. I live in the Czech republic, which has some kind of non-visa agreement with the USA (ESTA?), something much simpler and easier than regular visas, but you still need some kind of stamp. In fact, there was a discussion about this and how should be our EU membership leveraged in order to get a better position, but there weren't much of a agreement. I believe that old EU states (Great Britain first) weren't happy about the fact that there should be some common policy. (Indeed, Schengen isn't equal to EU, it isn't even a subset of it, there are non-EU countries included, and some EU states aren't members (Great Britain). But there isn't any common policy, both EU and schengen-wide.)