...but EASA doesn't have any oversight on any of their operations at all. By imposing that pilots need to be dual-licensed they have a measure of control over this.
But of course EASA has oversight on foreign operations in EU airspace.
The dual-licencing issue is just the result of lobbying from some British and Continental European flight schools and examiners wanting to make a quick extra pound / euro, nothing to do really with aviation safety.
Luckily legislation was drafted sloppily, so that enforcability is a bit of a problem. The effective implementation date also has been postponed a few times. Also, new management at EASA has become a bit more sensible.