Previously, search in a legal sense combined two elements that we've always blurred together:
1. Collection of data
2. Intepretation of the data.
So when a human searches, they are comingled. Light enters the eye, is processed into images in the brain, is elevated into consciousness and draws connections in the front cortex and elsewhere.
But an automated system can do it in two stages. The pictures could be recorded and never analysed.
The question is whether the act of searching includes both data gathering and analysis as inseparable parts or whether they are seperable. And if they are seperable, where does the search reside: in the data, or the analysis?
Reversing your analogy, the NSA approach is like the police having housefly-sized drones in every house, keeping HD video of everything that goes on. Most of the time, nobody sees it. The data is gathered but not analysed.
Is that search?
The issue here is indiscriminate copying of data from third parties through whom your information traveled. Under the government theory it is not a search (because nobody has looked at it), it is not a seizure (because you still have your data), and your person, house, papers and effects were not touched. Therefore it is an activity that lies outside the protection of the Constitutional phrase, The right of the people to be secure in their persons, houses, papers, and effects, against unreasonable searches and seizures, shall not be violated...
It's unfortunate that there is such a disconnect between real and virtual policies. People who can't handle the abstraction shouldn't be making decisions regarding it.