The original Signal can be reconstructed with much wider filters but they'll only work if the signal is perfectly periodic.
I was wondering what happens if the signal isn't periodic. It could go very wrong.
No, it does not have to be periodic. "Perfect reconstruction" only requires that the original signal sampled by the ADC sampled was
bandwidth-limited.
And with a realizable real-world reconstruction/interpolation filter, this bandwidth limit is not 0.5*sample_rate,
but lower. For the Rigol, it seems to be about 0.3*sample_rate.
Just make sure that the signal you feed into the ADC does not contain any frequency content above 0.3*sample_rate, and the interpolated waveform you see on the screen will be the same as the waveform sampled by the ADC (at least almost the same -- small residual errors are unavoidable in practice).
If you violate this precondition, perfect reconstruction is not possible and the resulting distortion is implementation-dependent.