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So inadvertently it looks like I discovered how this is done when playing with the SQL Server ODBC driver. It seems that Tableau does not use a native StdDev or Variance aggregation when using ODBC, instead it calculates it via first principles via the use of SUM, COUNT, POWER and SQRT. I didn't have POWER and SQRT scalar functions implemented so Tableau complained about the missing aggregations - I just implemented them and it now is able to generate the SQL to get at them. Problem solved!
Just thought I'd post this for any future explorers.