This name is a synonym of Osmorhiza mexicana Griseb..
The record derives from Tropicos
(data supplied on 2012-04-18)
which reports it as a synonym (record 1701365).
This name record (from Tropicos) was not included in version 1 of The Plant List. It is possible the same name was included from a different data source, to check this you can search for Osmorhiza brevistylis in version 1 of The Plant List.