As far as i know the wording in our OM A was required by the local authority that argued that according to EASA you may continue to DH, but with a NO DH approach you do not have any DH therefore you may not continue as there is no DH to which you can continue. Additionally the required visual segment for rollout and taxying may not be available and therefore the safety case isn't valid anymore.
I know that quite a few countries in europe handle that differently, which may or may not be an economic advantage. Given the low count of real CAT IIIb days in europe (without the UK) it doesn't seem to be a major issue though.
As for the ABP itself, yes the main definition is the OM for us, but in the following notes it defines 1000ft in absence of an OM or other check point as the ABP.