I was surprised because it goes against the principle of divide et impera. Apparently a divided Europe makes it easier for the USA and China to do whatever they want, and Russia too. Unless the EU with a skeptical UK is worse off than without it.

But I see your point. It's not American interests against European ones. It's to prevent a secession in a geographical space more and more dominated by some corporations and financial institutions. A secession would make it a little bit harder for them, but not so much IMHO, unless it spreads and the EU shatters (maybe because of the migrants crisis.)