I would not call this deceptive. The statement does depend on where you are now as to how 'Great' this aspect of the EU is compared to your country.
Living in the US, I am living in a union of states where I have the same right. I can move to any of the 50 states (and DC) and live there for work and be equal to those that have lived there their whole lives. This mobility of the workforce is a very important part of reducing unemployment. If the population is mobile and has the freedom to move from region to region, they can move to where the work is.
In the EU, most citizens can move to wherever they want in the EU for work, or for any reason without much restriction. There is talk of restricting citizens from new member states to prevent them all from moving to the higher paying countries. But the funny thing is, the EU did not need to enact barriers to keep people from moving from one country to another, as there were already natural barriers in place. Take language. almost each country in the EU has it's own language and I can tell you from experience, that your going to have an impossible time finding work if you don't know the language. Language matters for even trivial work. But that's just for starters. You are not in their 'system.' Not in the banking system. Not in their Social Security system.
Then there is the fact that you are in another country. You have to learn how things are done there. In the UK, they drive on the other side of the road and you'll have to buy a new car because yours has the streering wheel on the wrong side. They do not use the euro in the UK either. Nor is the Euro used in Sweden and in the new EU member-states. As you are not a citizen of that country, you can be excluded from public sector jobs, such as policeman, etc which is a shame since the public sector is normally the biggest employer.
As for border controls, the UK still has them for internal EU citizens too, but it is a formality. However, in a number of the countries, you will have to obtain a residence permit if your going to stay. And if you just want to move there and you don't have a job, you need to prove that you have enough funds to live without assistance as well as adaquate health insurance. This is setup to prevent movement of the poor (most likely from states with poor welfare to those with good welfare programs.)
That's one of the great things about working in the US. Sure, NY is very different from Arizona, and from Alaska, and Hawaii, but I can be confident that all the basics will be the same; The language, the currency, the social security, the tax system and Government.
Note: Fred has worked in a number of EU countries both as cargo ship crew and shoreside.