For BEagle, please remember that the part of the Birmingham AIP entry you quote is from the noise abatement section. Not making too much noise is good practice. However making too much noise by not complying with the airports wishes in that regard is not in itself dangerous or illegal. It is perfectly possible to exceed noise requirements on a daily basis and simply factor the charges into the operating costs.
While the dive and drive is not considered best practice these days, it is not illegal and provided that the procedure requirements are complied with it is not dangerous.
I would indeed be looking at the poibility that HON dme was being used in error as a distance from threshold reference. Would be looking into what navigation aids were briefed, set and identified during the arrival and approach phases.
Regards,
DFC