May I respectfully draw your attention to your example immediately under 'The accidental 'se' with olvidarse and suggest as a literal translation
'The keys have forgotten themselves to me'? This accounts for the perfect tense and the reflexive 'se'.
You also give examples of forgettibg things 'accidentally'. Can one forget things 'on purpose'?
With reference to your English literal suggestion to that sentence, we tend to use the most natural translation in English despite this not been literal, but I will pass that suggestion to our English team.
When we point out this in the lesson about the "accidental se" use in "olvidarse":
What we mean is, that even though olvidarse is always going to be unintentional, because we cannot control the forgetting, using this structure with "se" makes it somehow as if the person wanted to reduce his/her responsibility for having forgotten something.
So these two sentences have a slightly different nuance:
Olvidé las llaves. (I forgot the keys.)
Se me olvidaron las llaves. (I forgot the keys but somehow this wasn't my fault)
I hope this clarified it.
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