Good discussion here. I think what it comes down to is this. Passengers on a booking on one PNR have bags tagged with their own names but they are considered a pool such that if any of them does not show up then all the bags on that pool are offloaded. Notice how when you checkin together they are not meticulous in ensuring that each of you say exactly which bags are yours. This can also happen on separate PNR's where the checkin is pooled at checkin. In a pooled checkin - since all the bags are assigned "joint and several" to all the passengers, it seems perhaps that all the PAX have to be there to answer the questions together as PAX 1 may have goods from PAX 2 in their bags in their allowance and if the other PAX is not there - then they cannot confirm this. If you have to checkin at separate times to USA - it may be best is to split the PNR and then ensure you do not pool the two on checkin (an example of Pooling at checkin is done on Swiss where you can name another PAX not on your PNR to be checked with you on the online checkin - the system will then combine these to a pooled checkin).
Not sure if this makes sense - or even if this is what happens in practice - it just seems that for USA flights you must be the one to put your bags on the belt and it is unclear about if the whole group has to be there together. I will ask my connections at Swissport to see if they have any clarification.
Hope it all went well.