[echo_time]

This is incorrect - all of the protons align along the static (the strong 1.5, 3 , 9.4 etc Tesla) field, some point one way, and some the other - but they have all shifted so that they line up. The excite portion is a separate step, distinct from the static (B0) field. edit: distinct in some ways - the strength of the static field determines the RF used to flip the protons out of alignment.

[sigmoid10]

You are mixing up a few things here, but they are all missing the point. At normal body temperatures, their thermal energy distribution prevents most protons in a human from aligning parallel or antiparallel with the static field, even at MRI field level strengths of several Tesla. The excitation by the varying field, which only affects another one-in-a-million of those aligend protons, is indeed another step, meaning that even fewer protons actually get to experience the precession effect. So about one in a million protons gets aligned with the static field and less than one in a trillion gets to produce a measurable signal. But since there are so many of them, (~10^20 per mm^3 for water), you still get enough (about 1000 protons or so per voxel) to measure a signal at 2 Tesla. With higher field strengths you can get a bit more and thus more resolution but even at 10 Tesla you won't align all of your protons - not even close.