This name is a synonym of Rytidosperma pallidum (R.Br.) A.M.Humphreys & H.P.Linder.
The record derives from Tropicos
(data supplied on 2012-04-18)
which reports it as a synonym (record 25510648) with original publication details: Syst. Veg. 1: 336 1825.
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 Avena brownei in version 1 of The Plant List.