I was born and bred in a country speaking American English widely, it having been a US colony for almost a century. I was schooled in Belgian English, which leant heavily towards British English. In adulthood, I came to work for the British Embassy, and I guess it's fair to surmise that the British diplomats are among the best exponents of HM English. I then came to admire the precision of UK English even more. It's not only precise -- it is crisp and succint as well.
In the Embassy, the UK-based staff uniformly used the word 'orient' only as a noun (and never as a verb) -- to mean East; and it's only other derivative similarly used being the word 'oriental', another noun, meaning Easterner (Asian). 'Orientate' is a verb, THE verb as a matter of fact, to connote familiarity -- to familiarise, introduce, provide one's bearings, etc. Everything else follows from there: orientated, disorientate, disorientated.
Ergo, as far as I'm concerned, it is precise and confusion-free to use 'orient' only as a noun, and 'orientate' as a root verb. In the same vein, it would be sensible/ logical to use as an adjective the word 'disorientated' when one 'is puzzled', rather than 'disoriented' -- which, I agree, indeed seems to refer to 'somebody being thrown out of the East'.