Why just EU? The EU delegates can pressure US to cover anyone under the act not just EU residents. If US bends to EU's demands about privacy but doesn't treat rest of the world similarly then it says something about US.
EU "delegates" don't have what it takes to pressure the US on anything. It's usually the other way around. EU regularly bends to US demands, not vice-versa. E.g. providing the NSA with personal data for all airline passengers flying in or out of Europe...