I think it's a bit harsh to say not even close. I think it captures the idea pretty well.
The reason it's not perfect is because of your example, where a signal is not baseband. The extra leap required to understand that is amplitude modulation and demodulation.
Notice that to reconstruct the original signal of your example, you need to know the samples which are collected following the hypothesis of the sampling theorem, and you ALSO need to know the magic frequency 100MHz so that you can shift up your 2kHz bandwidth. That's the same setting as modulation.
The only concept missing, then, is recognizing that sampling can perform demodulation.
Demodulation via sampling isn't a weird side-case, that's at the core of understanding Nyquist and doesn't line up with the intuition that you just need to "sample each up- and down-deflection of a wave at least once"
I disagree with you. To be clear, "sampling each up and down deflection" is exactly the right idea in the case that you have no other information besides the samples (and besides knowing the hypothesis of the sampling theorem is satisfied). To use the more general version of the sampling theorem, you in addition need to know the center frequency (100 MHz in your example), otherwise you cannot reconstruct the signal. So already the setting is slightly different. You need an additional assumption.
The reason it's not perfect is because of your example, where a signal is not baseband. The extra leap required to understand that is amplitude modulation and demodulation.
Notice that to reconstruct the original signal of your example, you need to know the samples which are collected following the hypothesis of the sampling theorem, and you ALSO need to know the magic frequency 100MHz so that you can shift up your 2kHz bandwidth. That's the same setting as modulation.
The only concept missing, then, is recognizing that sampling can perform demodulation.