In the bank analogy it's obvious that the bank's representation would be present and witnessing the use of their master key to ensure that only the box in quest

In the bank analogy it's obvious that the bank's representation would be present and witnessing the use of their master key to ensure that only the box in question was searched, and that's all that Lavabit asked for. We take it for granted when it comes to a physical search so why should they have unsupervised access to everything for a digital one?