That description from BA might well be how they would like to load, unload and deliver bags, but I am certain it does not work that way at all. My bags always come off last regardless of how they are tagged, where they were loaded or what class of travel I purchased.

My bags which connect in LHR always make it to the same destination as me but usually with a delay factor of 24-72 hours. I just received my 3rd bag from SFO 12/08 here in FAO yesterday 15/08. My Airtags told me on landing in FAO the all 3 bags were still at C gates in Terminal 5, so I just went home to file the missing bag reports as usual.