The EEC was enough for free trade agreements. And you don't have to be in the EU to participate in the Schengen treaty/zone (for visa-free travel). Iceland, Norway, Liechtenstein, and Switzerland are not in the EU, but part of Schengen, while Cyprus and Ireland are EU countries, but not in Schengen. The fact that people conflate the EU with these things is simply that this has been the narrative that was pushed. Also, people who were e.g. against the EUR at the time were vilified as right-wing extremists, same as anyone who criticizes the EU today.