While I agree with most of what is said in user6726's answer, as it is currently written, I disagree with the ultimate conclusion to the title question so feel the need to write my own answer.
Copyright law—and law in general—is usually territorial and does not apply to acts committed abroad. Extraterritorial jurisdiction tends to be reserved for serious crimes such as terrorism, trafficking, maritime piracy, and almost exclusively in US law, tax. Therefore, copyright law does not follow Abby to a foreign country, and it does not matter where content originates.
In Morrison v. National Bank of Australia, the Supreme Court provided a strong affirmation of the presumption of territoriality in Part III-A stating:
When a statute gives no clear indication of an extraterritorial application, it has none.
For this principle applied specifically to copyright law, see for example the Ninth Circuit Court of Appeals case Subafilms Ltd. v. MGM-Pathe Communications Co.:
Because the presumption has not been overcome, we reaffirm that the United States copyright laws do not reach acts of infringement that take place entirely abroad. It is for Congress, and not the courts, to take the initiative in this field.
Do note though that importation (Kirtsaeng v. John Wiley & Sons, Inc., Supreme Court), or even being available online (Spanski Enterprises, Inc. v. Telewizja Polska, S.A., D.C. Cir.) can bring the alleged infringement into the territorial reach of US copyright law even if most of the activity is occurs abroad.
With regards to the EU, the best case I can find is Pinckney v. KDG Mediatech AG, C-170/12 which in paragraph 39 states:
First of all, it is true that copyright, like the rights attaching to a national trade mark, is subject to the principle of territoriality. However, copyrights must be automatically protected, in particular by virtue of Directive 2001/29, in all Member States, so that they may be infringed in each one in accordance with the applicable substantive law.
and concludes (emphasis mine):
Article 5(3) of Council Regulation (EC) No 44/2001 of 22 December 2000 on jurisdiction and the recognition and enforcement of judgments in civil and commercial matters must be interpreted as meaning that, in the event of alleged infringement of copyrights protected by the Member State of the court seised, the latter has jurisdiction to hear an action to establish liability brought by the author of a work against a company established in another Member State and which has, in the latter State, reproduced that work on a material support which is subsequently sold by companies established in a third Member State through an internet site also accessible with the jurisdiction of the court seised. That court has jurisdiction only to determine the damage caused in the Member State within which it is situated.
So in the EU, even though copyright law is harmonized to an extent, copyright is still territorial to each Member State within the EU, though it would have been nice to find a reference that this also applies external to the EU.