Whilst this is true, I would hope that the transformer has a fuse in place to maintain the integrity of the magic smoke containment devices. And with excessive load, the winding from the unit being powered to the live input will be the one most likely to fail so this will cut the power to the device. The winding in parallel with the output is less likely to fail under excessive load as the voltage across it will reduce as the load increases.
Originally Posted by polyglot
I do agree with you that an isolated transformer is the best option and personally, I think that should be the only option available but as we know, these days things are built down to a price rather than up to a quality so the cost effectiveness of an auto-transformer wins.
I think the OP was worried about the general idea of plugging into a transformer. With the transformer suggested, there should be no problem.