It's the theory vs. practice part that can get you on BA. I split accrual all the time on other carriers and only BA (it's not a OW issue as AA can get it right quite easily) has a problem with it.
I asked for my FF# to be taken out of the reservation. I asked at JFK check-in to use BA and was told that it can only be entered JFK-LHR-BLR as it was a directly connecting flight, but I could ask for it to be changed in LHR. I did, at the arrivals lounge. I then entered AA at checkin in BLR and was told I would have to change it in LHR. I did, at the Gate1 Lounge. Bottom line is I have boarding passes with the correct # for each sector but LHR-BLR went to the wrong program (says AA# on BP, accrued to BA).
I will say this has happened in the past and BA has always been happy to sort it out and it involved sending a fax and "declining" the sector milleage accrual in question and then claiming it back on AA manually. A pain, but doable. This time however, my LHR-JFK flight kicked me over the silver threshold and "reset" my membership year. Unfortunately BA claims they can't make any changes to a previous membership year and I'm stuck.
Luckily I have a flight to LHR that I could switch over to AA in First that will push me over the EXPLT threshold, otherwise I was counting on that LHR-BLR mileage to do so.