Nero will insert the AUDIO_TS folder by default if the DVD Video project type is selected.
It's possible to override this but I can't see any reason for doing so.
According to the DVD specifications the AUDIO_TS is required for compatibility reasons however in practice it's almost universally ignored by standalone DVD players.
It's a subject that regularly resurfaces as to whether or not the AUDIO_TS folder is required at all on DVD Video discs as even some commercial discs have don't have it.
Personally my view on this is that since it takes up virtually no space, and there's no advantage in excluding it, then it should always be present.
I think you're right in suspecting a media problem though as off the top of my head I can't think of any other reason why it would play in one PC and not another.
In fact if it plays in one PC then it should in theory play in any other PC providing the media is okay.
Bit of a mystery this one.