Having lived in both hemispheres, I can confirm that in the main it is all true. In the absence of any other factors water develops a spin opposite to the other direction, in general.
On a visit to Kenya, on the equator I also experimented but could not perform the experiment sufficient times to be conclusive in the week available. 22 years in the UK and 18 years in South Africa provided a robust experimental window
Seems to be unique to North American plumbing. European toilets flush with no swirling at all
I would hazard a guess that one contributing factor is that the initial water level in European bowls is much lower than in their American counterparts. Couple that with the typical European straight "wash-down" design vs. the usual American syphonic action, and that probably accounts for it.
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