sampling guarantees periodicity
Not exactly. Sampling in one domain guarantees periodicity in the other domain. So sampling in time creates a periodic spectrum and sampling in frequency creates a periodic time signal. Or the other one around: a periodic time signal has a discrete spectrum and a periodic spectrum has a discrete time signal.
That's why ...
Aperiodic signal will also have certain band of interest which you actually try to sample. This band of interest repeats itself, which can be observed in frequency domain. Thus, your aperiodicity has now converted into periodicity.