I dont see how this answered the original question of the poster.

He was quite clear: the value of the predictions coming out of RF do not
match what comes out of the predict function using the same RF object and
the same data. Therefore, what is predict() doing that is different from RF?
Yes, RF is making its predictions using OOB, but nowhere does it say way
predict() is doing; indeed, it says if newdata is not given, then the
results are just the OOB predictions. But newdata=oldata, then
predict(newdata) != OOB predictions. So what is it then? 

Opens another issue, which is if newdata is close but not exactly oldata,
then you get overfitted results?

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