This is odd, as it seems to have come up also on the AA tube diy forum.
A shorted turn is most common (and easiest to visualize) in toroidal transformers. If you imagine your doughnut mounted to a metal chassis plate with a bolt and another metal plate up top, you can see that nothing completes a loop around the core of the transformer. If you decide to make the mounting more secure and you pass the mounting bolt through the other side of the chassis, or you add a bracket from the top of the transformer to the side of the chassis, now you have a complete loop around the core of the transformer, and hence a shorted turn.
(https://forum.bottlehead.com/proxy.php?request=http%3A%2F%2Fwww.amgistoroids.com%2Fassets%2Fimages%2Ftoroidal-tech-fig-02.jpg&hash=87d20e5e7e794761c2319f7a60b6063629b8241e)
In the photo above, you just need a loop that wraps around that isn't an actual winding.
In an EI transformer, the primary flux paths are essentially inaccessible to any reasonable type of cover.
(https://forum.bottlehead.com/proxy.php?request=http%3A%2F%2Fwww.amgistoroids.com%2Fassets%2Fimages%2Ftoroidal-tech-fig-01.jpg&hash=4a468004cede1da674a111a7670b3a8b92b1dac3)
In the EI transformer, windings wrap around the inner piece of the diagram above, so creating a shorted turn would involve a cover that actually wrapped around the bobbin between it and the stack (this is not to be confused with a Faraday shield).
(https://forum.bottlehead.com/proxy.php?request=http%3A%2F%2Fsound.westhost.com%2Fxfmr11-3.gif&hash=c494640faf5c41b7d98bd18d5628bd04424597cb)
A cover around the transformer is intended to act as a shorted turn to the leakage flux (the outer loop), but it doesn't create a loop in the interior. If you have a Seduction laying around, you can observe that the copper wrap goes around the outside of the transformer, over the bobbin, but does not create a shorted turn.
(https://forum.bottlehead.com/proxy.php?request=http%3A%2F%2Fsound.westhost.com%2Fxfmr13-4.gif&hash=7a1ef676b511f839e3301b514f01036ffd5b569b)
(Sorry Jim, I wish I had better words than photos, but not today
)