The AA sockets, as specified and originally installed, are identical to those on an iPod, MP3 player, Bose headset, etc. 3.5mm O.D.

The problem, especially on the 767's, is that they are old, worn and poorly maintained. The "mini-phone jack" relies on a certain amount of friction to be maintained between the mating plug and jack and are only rated for a certain number of insertions by the manufacturer. All this, together with the fact that many who fly on airlines do not take the same care that one would with their own personal electronics, result in the need to, as you say, connect it "jut so" to get it to work.

I'm convinced this is one reason why CX uses the larger 1/4" plug as it provides a much better mechanical and electrical connection over time.