A salutory tale.
It seems we are off on a few incorrect tangents, however?
1) Reading 'Lesson f' suggests the Captain was not an ex-pat, so some of the comments here may not be applicable
2) It does indeed sound like the 'alt*' event which I know from the 737 well. A low-level level off is by no means unusual and needs to be carefully briefed due to this. It can be common in Tel Aviv. It is easily handled as a crew.
3) The 'CVR download' in JFK would be a waste of time unless our poster had pulled the CB which would, it seems, have been a death sentence.
4) The intitial reaction of the Captain in disconnecting the A/T is understandable but not excusable. The Captain should have expected, briefed and known what would happen. It is "Lesson 1" in how to deal with automation - if it appears to be malfunctioning turn it off and revert to basic flying skills The latter part did not happen.
The demonstrable existence of such fear of reporting is of serous concern. Surely an FDR would be fitted and that could have been downloaded? If we are in yet another 'culture/status' driven area of operations then some international body needs to wake up.