tl;dr: Here comes a motivation/background for this question; perhaps you would like to skim ahead to the
We know that there is a lie behind a lie: In the first film we learn that the world of Thomas A. Anderson was a dream world, it was a lie created by the machines to imprison human minds. The atmosphere in that film is a very hostile one, where a relatively uncomplicated adversarial situation is depicted. Clear sides in a war.
However, we then learn that this is orchestrated by the Architect and the Oracle, because of what they learned about human nature (I wont go into those reasons).
If we think about this, everything we see in "The Matrix" (the film) goes according to plan for the machines (well, for the higher ranks at least, certainly not for Smith, but that's a different story). If we bring this to a logical conclusion it gives a beautiful explanation for why the first docbot (sentinel-like machine) Neo encounters when he first wakes up:
doesn't instantly kill him, but conveniently flushes him out for the Zionists to recover him. You could even argue that it recognises him as The One, but that's not even a necessary observation.
Clearly, if the machines would be so clearly in war with the free humans, they would have at some point figure out to kill the humans (or even recycle them, as they do with naturally occurring deaths) that wake up in their pods, instead of flushing them out.
Clearly, that machine is more than capable of killing a defenceless human:
This means, the machines have a perfectly good reason to allow humans to be rescued so easily (think about how trivial it was to get Neo to Morpheus inside the Matrix and how trivial it was to extract him from the power plant).
But this must be entirely daft from the humans' perspective, as they live under the assumption of a cold blooded war and merciless enemies. What explanation do they (!) have for this seemingly inexplicable behaviour of the machines?