It is untrue that the natural English or is clearly and uniformly disjunctive. If it were, it would be impossible to add "or both" or "or whatever" to an or clause, or to make a list of more than two items, as in StoneyB's examples:
“Help yourself to chicken or ribs or chili or whatever strikes your
fancy” and “I like Dickens better than Trollope or Scott or Thackeray”
RJB is correct that
how a person uses 'or' is very much defined by their perception of
what they mean, rather than by any formal rules of the English
Often we use or to convey a feeling of subjective doubt:
He speaks French, Spanish, Portuguese and German or Finnish, I
The point is not "either G/or F"; the point is "maybe G, maybe F...". And while we tend to use "either.. or..." to strengthen the sense of "not and", this is a matter of degree not kind. There's a nice page on contract drafting here and StoneyB's superb coffee & cake example makes it clear that context is key, (or) perhaps even king.
Note also that English uses or in negative sentences such as the following:
Bob's not in his room or his study.
Clearly in logical terms what is meant here is "Bob is not in his room and Bob is not in his study". Natural English does not use and because the conjunction falls within the scope of the negation (and it's obvious that Bob can't be in both places at once, so why say it?). In more formal English, we would say he is neither in his room nor in his study. Some languages, such as Chinese, use a positive conjunction and two negative particles to convey this idea (他不在房間也不在書房).
But I'd agree that, apart from contextual considerations, the default meaning of or does tend to be disjunctive. Frequently when translating the Chinese or, I have to use and in English because the or is insufficiently inclusive.