The observed proportionality between the centripetal contribution of the
dynamically insignificant HI gas in the discs of spiral galaxies and the
dominant contribution of DM - the "Bosma effect" - has been repeatedly
mentioned in the literature but largely ignored. We have re-examined the
evidence for the Bosma effect by fitting Bosma effect models for 17 galaxies in
the THINGS data set, either by scaling the contribution of the HI gas alone or
by using both the observed stellar disc and HI gas as proxies. The results are
compared with two models for exotic cold DM: internally consistent cosmological
NFW models with constrained compactness parameters, and URC models using fully
unconstrained Burkert density profiles. The Bosma models that use the stellar
discs as additional proxies are statistically nearly as good as the URC models
and clearly better than the NFW ones. We thus confirm the correlation between
the centripetal effects of DM and that of the interstellar medium of spiral
galaxies. The edificacy of "maximal disc" models is explained as the natural
consequence of "classic" Bosma models which include the stellar disc as a proxy
in regions of reduced atomic gas. The standard explanation - that the effect
reflects a statistical correlation between the visible and exotic DM - seems
highly unlikely, given that the geometric forms and hence centripetal
signatures of spherical halo and disc components are so different. A literal
interpretation of the Bosma effect as being due to the presence of significant
amounts of disc DM requires a median visible baryon to disc DM ratio of about
40%.Comment: Accepted by A&A (Paper I