I deliberately placed the word 'Bastions' in inverted commas because I don't think they are - based on heritage possibly but do they offer the best education? If an exam factory is what you want then maybe....if not then no (in my opinion).
International School. Hmmm...I was born in the UK but was educated in Australia then HK in what I consider to be an international school (Island school 1970 - 1982) mainly because of its mixed pupil body with regard to race and culture. Curriculum was British though. Was that a good thing? At the time I think it was. But then it was the tail end of the colonial period/expats on tour etc. Was it International? I think so.
I worked in an international school (by name) for seven years in France (a brand new school that opened in 1999 - shell primary programme, iGCSE and the IB Diploma offered). Spoken languages were English and French (with mainly British and French Staff but also German and Spanish too). International by name, school population 2/3 British and the remainder Australian, American, German, French, Canadian, Korean, Chinese...but actually more British in approach than international (again, my opinion).
In between I have worked in a few UK independent schools and they do many things well but are not international, by school population or curriculum. In fact, at times the joke in one school was that we were international because we had students from Surrey, Berkshire and Kent
As you outline Tasebo, being an international school by name is different to actually having a pedagogic approach that is international.
So, what makes a school international? Location aside, I think it has to be curriculum led - one that embraces elements of good practice from around the globe - and one that delivers the content in more than one language. How you then sieve that through to get your final curriculum delivery via exam delivery/parent expectation so that youngsters go on to University in a global market place is important.
I'm quite lucky in a way as I am married to French girl, our two bi lingual daughters have been educated in state and private schools in The UK and France and our eldest is off to Toulouse for Uni to study languages. Our youngest joins us in CH for our new journey in an international school. It will be interesting to see how that unfolds.
There are a lot of cultural assumptions going on when individuals assign meaning to words such as "international" therefore it is easier and less problematic to accept schools at their word when they say that they are.
The MYP/IB, to the best of my knowledge and experience, is the closest to what Wile7 defines as an "international" approach to educating at upper ages, and even that seems a bit of a need for nomenclature more than a pedagogical system/philosophy.