Missed baggage due to customs check delay

Do not miss your flight if you aren't sure. If you get to the point where it is nearly time to board the flight and this hasn't been resolved, proceed to boarding and raise the issue with personnel at the boarding desk.

The call you received suggests taking the flight is the right course of action, but someone at the desk might be able to give you more help. If you aren't able to get a definitive answer, I would probably board the flight based on the information in the call.

If you have some extra time before boarding, you might:

• Try the office of your connecting airline. BA has only a few flights into Boston, and thus probably has a limited presence in the airport. But your onward travel will be on a US-based airline, which probably has more staff in the airport, and may have longer hours. I would check to see if they can help you.
• Call BA about the problem. They will have a US helpline, though it may have limited hours and not be open. If it is a 1-800 number, you can usually call these free from a pay phone.

I would say it's not a totally irregular occurrence for a passenger not to pick up luggage prior to a connecting flight after entering the US. Reasons would include immigration delays, as suffered by the OP, and passengers being confused about the fact that they need to pick up bags and recheck. Also, some passengers may be more worried about catching a connection that they are about their luggage.

e.g. from Flyertalk:

I'm on an ex-EU trip and I've just flown OSL-LHR-DEN-LAX.

Unfortunately, due to my stupidity (I knew this but I forgot) and to BA's failure to instruct me (no one at Oslo or Heathrow informed me), I didn't collect my bag and checked it in again at Denver. I've reported to AA in LAX, and they said they'll deliver it to my hotel.

Or this one:

I had this happen once on AA, basically my flight was late and my luggage didn't come up with the rest so seeing has how I was going to miss the last connecting flight of the night I asked if I should wait for the bag or go on through. I was instructed by staff in the arrivals hall at ORD to go on through and then file a lost luggage claim once I reached MCI. I did just that and three days later my bag was delivered to my house an hour away from the airport.

Also an old thread with some anecdotes.

I would suggest that airlines have procedures for handling bags that are left on the carousel and have already been tagged onwards. As @dan1111 says, it makes sense to contact BA and/or your onward carrier to confirm the status of all your bags as soon as possible.