Airlines usually treat the sort of bag that has a zip off daypack as one piece of baggage. So it is in line with this to treat this ski bag with zip off other bags as one piece of baggage also.
On several previous occasions BA has treated this as one bag.
In addition, BA specifically allow other items packed with the ski bag, as I pointed out.
The VCE check in assistant was contrary to the spirit of the BA baggage rules, contrary to repeated other BA staff practice and contrary to how they treat other bags with detachable parts or even disparate items wrapped up together (items plastic-wrapped together).
I don't consider your (frequently dispensed) contrarian Devil's Advocacy is realistic or helpful here.