I hate to challenge the renowned master of toilets himself, but Bemis only makes toilet seats. Companies such as Crane, American Standard, and Kohler manufactor the toilets themselves.
The real question on toilet choice is the litres per flush. In America, the limit now is 6 litres per flush. There used to be no limit, and toilets had from 9-12 litres per flush.
As a result, many consumers have kept their old toilets so that they have more flushing power. This way the toilet can handle massive dumps by releasing more water.
However, newer brands are trying to make the toilets with 6 litres per flush more efficient, using techniques such as Gravity or Pressure Assisted flushing systems.
So the real question is, "How many litres per flush do the White House toilets have?" I'm betting they are 6 litres. My toilet is better.
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