We present new Chandra X-ray observations and detailed astrometry of the field of the type Ia supernova 2007on, for which the detection of a likely progenitor in archival Chandra data was recently reported. No source is detected in the new Chandra images, taken six weeks after optical maximum. We calculate a 90-99% probability that any X-ray source near the position of the supernova (SN) is fainter than in the pre-outburst images, depending on the choice of aperture, which supports the identification of the archival X-ray source with the SN. Detailed astrometry of the X-ray and new optical images, however, gives an offset between the supernova and the measured X-ray source position of 1.15+/-0.27". Extensive simulations show that the probability of finding an offset of this magnitude is ~1%, equal to the (trial-corrected) probability of a chance alignment with any X-ray source in the field. This casts doubt on the identification of the X-ray source with the progenitor, although the scenario in which at least some of the observed X-rays are connected to the supernova may be the least unlikely based on all available data. After a brief review of the auxiliary evidence, we conclude that only future X-ray observations can shed further light on the proposed connection between the X-ray source and the progenitor of SN 2007on, and thus whether an accreting white dwarf scenario is truly favoured for this SN Ia.