Instead of trying to recreate a set of rules defining what an anime is, we have to identify at least two reliable sources to consult where the "it is not an anime" exception is moved.
The first two I can think of are:
- Anime News Network encyclopedia
Anime News Network apply these rules in the What is anime section of their FAQ:
anime is animation that is primarily produced and conceived in Japan. This includes animation conceived in Japan that has portions outsourced to other countries, but does not include animation primarily produced outside Japan and with the animation outsourced to Japan. It does however include animation that is co-conceived inside and outside of Japan and at least partially produced inside Japan.
ANN editors identify two technical definitions of anime, 1) by origin and 2) by style. They agree to "by origin" definition.
Wikipedia excerpts are cited in a previous answer I don't repeat here. The article is useful while defining the controversy about origin vs. style issue, but the very methods used in Wikipedia to identify what an anime is for Wikipedia are written in the Anime and manga WikiProject page (the Wikipedia equivalent of Meta SE), where they clarify:
Although its scope is broad, this project maintains an essential focus on anime, manga and related merchandise originally meant for consumption in Japan. This does not include works with incidental or minor association. Animated or printed works produced for consumption outside of Japan that nevertheless draw on or are similar to Japanese media in terms of content or form (such as Chinese animation, Korean animation, manhwa, manhua and Western manga-styled comics such as Gothic Sports and Peach Fuzz) do not fall under our scope.
Both Wikipedia and Anime News Network apply the "per origin" definition. First answers on Anime SE about this topic highlights a good consensus about this definition too. But to avoid controversy we have to rely to external, reliable sources like these when this exception is moved about a particular title.
Applying this rule to Batman: The Animated Series:
Batman TAS is not an anime.