There are 4 things not to be mixed here:
1. the "aliasing" creating the fake artifacts/spurious (caused by hw&sw because of "BW vs. sampling rate")
2. the "sinc" function used for "creating the nice pictures" via the "sinc interpolation" as seen on the LCD screen (each discrete point sampled is multiplied by sinc function and all that results are added, thus you get "additional points in between", you draw them all on the screen thus you see a solid line instead of just several sampled points, like 5 points for example)
3. the process of a "reconstruction/filtering of a square wave" with help of FFT, like sqrwave->fft->filter->ifft->sqrwave
4. the "ringing" of the hw circuitry (caused by steep filters, unstable circuits, impedance mismatch)
Edit: typos..