The OED has examples of the intransitive obtain dating from as early as 1441, but gives no specific etymology for this use.
However if you look at the general etymology, which indicates obtain coming to English via Norman-French it is instructive. Particularly look at the the classical Latin. Included in the English meanings of obtinēre are words such as win, prevail, hold, possess, to be prevalent, customary or established.
Etymology: < Anglo-Norman obtenir, optenir, optiner and Middle
French, French obtenir (strong stem obtegn- , obteign- ) to gain, to
achieve (1283 in Old French as optenir ), to be victorious (c1380), to
win (15th cent.), to succeed in attaining (c1500), to subsist (c1508),
to hold, occupy (a1525) < classical Latin obtinēre to gain, to
achieve, secure, to win, to be victorious, to prevail, succeed, to
hold, possess, occupy, to be prevalent, customary, or established, in
post-classical Latin also to conquer (from 8th cent. in British
sources), to arrive at a place (11th cent. or earlier) < ob- ob-
prefix + tenēre to hold, keep (see tenant n.).