Pálinka can only be manufactured in Hungary due, primarily, to legal reasons.
It is often referred to as “pálinka law” which is based on regulatory requirements of generic fruit spirits set by Hungary and the European Union. According to this law, an alcoholic beverage can only be called pálinka if:
Because of this strict description of what does and does not constitute true pálinka, many popular Hungarian alcoholic products were rebranded as szeszes ital, or “spirit drinks.” Even traditional pálinkas mixed with honey were re-categorized as spirit drinks — or liqueur if the sugar content exceeds the required limit.

Pálinka is traditionally made from a mash of ripe fruit. However, the law doesn’t control the addition of other non-concentrated fruit juice, and also allows the use of fruit pulp. Dried fruits are not allowed or used in the mash but may be used in the aging process of the liquor.
In 2008 the EU accepted pálinka as a Hungarian specialty, thus limiting its production to Hungary (and four provinces of Austria for pálinka made from apricots). This did cause some confusion for neighboring countries, as some claimed that fruit growers would be required to pay Hungary a royalty. This isn’t true, however. It’s the brand, “pálinka” that is protected by Hungarian and EU law, thus restricting outside fruit producers from using the brand “pálinka” for their products. They can, however, produce fruit spirit drinks and sell them under different names.
An interesting side note here is that historically, pálinka was distilled in the former Kingdom of Hungary, most of which is outside of present-day Hungary.