Just go with what the checkin staff tells you...
I just flew LAS-LAX-SFO-LHR-DUS on AA and BA (two different tickets) and my checked luggage made it all the way despite being searched by TSA at some point. BA lost my Bags twice on a non-stop LHR-FRA flight so I was quite concerned (and asked BA staff to verify they're in posession of my Bags at SFO and LHR), but despite all those connections, there was no problem at all.