To the lay person, 'Bengal Tiger' is the same as saying 'Tiger', and zoos might just go along with this. While there just might be some pure Indian Tigers outside the subcontinent, it's highly unlikely, as most have White Tiger blood, which was heavily contaminated with Siberian [Amur] genes over the years in the effort to produce bigger & more impressive animals. There's a potential research project here: DNA test all the Tigers outside India & see what's what. O bviously there would be pure Sumatran, Amur & perhaps Chinese [or is it Indo-Malayan?], but there might be remnant pockets of perhaps even Javan genes.
Idea: has anyone ever looked for Cape Lion genes in the generic zoo Lion population?