I truly think that in the cases where the buzzing stops when reorienting the cord that the "problem" has been temporarily disturbed. I suppose that it could be proven by putting a mark with a sharpie or something on the cord and seeing if the same way works every time, but I don't think it will. Here's why:
Polarity results from the fact that an electrical circuit has a negative and a positive pole. Direct current (DC) flows in one direction, resulting in a constant polarity. Alternating current (AC) flows half the time in one direction and half the time in the other, changing its polarity 120 times per second with 60-hertz current.
http://www.lincolnelectric.com/en-ca...ty-detail.aspx
Therefore, which way a non-polarized plug is in the wall is less relevant than it seems at first.
If you're getting a buzz, there's some electrical problem that needs to be addressed. The most likely place that your (hopefully former) repairman didn't check is at the backside of the male plug. That's the easiest place to overlook (It's accessed via the bottom of the machine under the "panel", or you can remove the screw on the outside of the plug and gently pull it outward a little), the easiest place to ground to the body of the machine, and the "hardest" to check - mostly because of clearances making it hard to maneuver. The process is easy.
Slightly wet hands (just came back from the washroom? Have a little water on your hands from the glass of water beside you? Spilled coffee on yourself again - no wait. That one is me.), cuts, pacemakers, all of it can lead to a really bad situation when added to a machine that's causing a buzz, tingle or shock.
I service enough machines that I know that there is liquid around machines quite often. I had coffee or tea to clean off the electronic machine I serviced yesterday, spilled all over the bed and allowed to dry!