ResetEra forums seem to indicate that the official statement seems to be having an actual effect. Xbox wireless controllers come from Microsoft so it is almost impossible to find them online.
Although the report cites France and the Netherlands as examples, the same thread confirmed that the standard controller was not available in other countries, particularly Italy. The official battery packs cannot be shipped directly, in the same manner.
The Xbox controller was not available in Italy, according to our tests. It is very easy to use the Elite and other third-party pads.
Official controller for Xbox one.
The controllers are not sold on Amazon.com or GameStop in the USA (even if they have been used or refurbished). However, you can purchase it from Target and BestBuy.
It is not clear why the Xbox controllers are so scarce. Some believe that Microsoft deliberately runs out of stock because of a revised pad with minor internal changes. This is a bit like the consoles. We will have to wait to hear from Redmond to be certain.