This seems bizzare, although for the US government to be able to track all those envelopes to their destinations, they would realistically have had to be prepared - I genuinely do not think that they have the resources to track 'everything, everywhere, all the time'.
So IMHO, unless UBS intentionally wanted to reveal the identities of their clients, marked all their envelopes and then tipped off the US that they were doing this, I would be sceptical about how many of these would ultimately be traced.
Of course, Swiss authorities tipping off the yanks
appears to be popular at present, so who knows...