Context. Recent accurate abundance analyses of B-type main sequence stars in the solar vicinity has shown that abundances derived from these stellar objects are more homogeneous and metal-rich than previously thought. Aims: We investigate whether the inhomogeneity of abundances previously found in B-type stars in the Ori OB1 association is real (hence a signature of enrichment of the newly formed stars in an induced star formation scenario) or a consequence of intrinsic errors induced by the use of photometric indices to establish the stellar parameters prior to the abundance analysis. Methods: We obtained a new (improved) spectroscopic data set comprising 13 B-type stars in the various Ori OB1 associations, and performed a detailed, self-consistent spectroscopic abundance analysis by means of the modern stellar atmosphere code fastwind. Results: We detect systematic errors in the stellar parameters determined previously which affect the derived abundances. Once these errors are accounted for, we find a high degree of homogeneity in the O and Si abundances for stars in the four Ori OB1 subgroups. The derived abundances are in very good agreement with recent determinations in other B-type stars in the solar vicinity. We also compare our results with those obtained for the Sun during the epoch of the ”solar crisis”, and the Orion nebula. Based on observations made with the Nordic Optical Telescope, operated jointly on the island of La Palma by Denmark, Finland, Iceland, Norway, and Sweden, in the Spanish Observatorio del Roque de los Muchachos of the Instituto de Astrofisica de Canarias.Tables 5 to 18, and Fig. 8 are available in electronic form at http://www.aanda.org