This name is a synonym of Linum rigidum var. berlandieri (Hook.) Torr. & A. Gray.
The record derives from Tropicos
(data supplied on 2012-04-18)
which reports it as a synonym (record 50120647) with original publication details: Reise Nord-America 2: 431 1841.
Full publication details for this name can be found in IPNI: http://ipni.org/urn:lsid:ipni.org:names:544332-1.
This name was in version 1 of The Plant List, record tro-50120647.