Entirely. The allusion is to augurs who divided the heavens into four parts. Among the Greeks the left hand was unlucky, and the right lucky. When all four parts concurred a prediction was certified toto coelo. The Romans called the east Antica, the west Postica, the south Dextra, and the north Sinistra.
“Even when they are relaxing those general requirements ... the education differs toto coelo from instruction induced by the tests of an examining body.” —Nineteenth Century, January, 1893, p. 23.
Source: Dictionary of Phrase and Fable, E. Cobham Brewer, 1894