No, his analogy was perfectly valid. In fact before I saw it I was going to make exactly the same point. The relationship of member nations to the EU is exactly analogous to multiple levels of government in those matters over which the EU has jurisdiction, and the dislike of the EU by some is exactly analogous to why many Americans dislike the federal government but are loyal to their state or local governments.
There is nothing magical or absolute about national sovereignty – it is diminished every time a nation signs a treaty or accord or any other international agreement. It is diminished by every member nation of the UN, whose members agree to abide by the rulings of its many agencies, councils, and courts. We do this because it’s in the common interest to have shared values and some level of international governance. Of course wingnuts also object to the UN, which is ironic because the Americans who rail against the UN undermining the sovereignty of the United States are usually the same wingnuts who hate the federal government.
If there is any argument to be had here, it’s about the question of whether or not the EU is beneficial overall. From what little I know of its long history and incremental evolution, going back to the Common Market and then the EEC, it seems that it is. It’s indisputably the case that much of the “leave” vote was cast for very, very stupid reasons, the kinds of reasons that Donald Trump would approve of, and indeed has just bloviated accordingly.