First, I would like to say that President Obama DID say it was a choice the British people must make, but it unfortunately drowns in the midst of all the other words relating to almost begging Britain to stay.
Let's make a point about legal systems first.
In the article State vs. Federal Law: Who Really Holds the Trump Card? we read the following about the difference between Federal vs State laws:
There are two basic levels in the U.S legal system: federal law and state law. A federal law applies to the nation as a whole and to all 50 states whereas state laws are only in effect within that particular state.The principle above has annoyed Americans numerous times, even though it is a principle that has reigned for many years in the United States of America.
If a state law gives people more rights than a federal law, the state law is legally supposed to prevail. This means state law will always supersede federal law when the person in question stands to gain more from the state law, right? Wrong. The law that applies to situations where state and federal laws disagree is called the supremacy clause, which is part of article VI of the Constitution. The supremacy clause contains what’s known as the doctrine of pre-emption, which says that the federal government wins in the case of conflicting legislation. Basically, if a federal and state law contradict, then when you’re in the state you can follow the state law, but the feds can decide to stop you. When there is a conflict between a state law and federal law, it is the federal law that prevails. For example, if a federal regulation prohibits the use of medical marijuana, but a state regulation allows it, the federal law prevails.
However, in the EU, the principle of EU-laws taking precedence over national laws, and not even requiring any national debate before having to be implemented in member nations is new to European countries. So new in fact that many are baffled when you tell them that up to 60% of laws are coming directly from the EU. You might as well end national parliaments is the logic many feel strongly about when it comes to the EU.
So in that light, I think it's fair to say, Obama's statement is one-sided, because he fails to acknowledge exactly WHY both Britain and Denmark ARE dissatisfied with many aspects of the EU. Danish PMs have failed to act on that negative feeling, and it lies at the foundation of why many referendums end up 50-50 when it comes to voting about EU-matters.
But IF President Obama was not made aware of this aspect of the EU, it might very well lie at the root of why he talked as he did. The American system hasn't understood much about foreign policy since the death of former President Nixon (who did function as advisor for many Presidents), and it might be a good idea to study the whole picture before talking as one-sided as he ended up doing...