Is this statement contradicting with the band-limiting theorem?
there is some choice of words i would do differently.  

yes truncating the infinite bandlimited function makes it time-limited and then band-unlimited.  but truncating it to an integer number of periods still allows one to fully describe it with discrete samples.  

a periodic function can be described with a Fourier series.  the Fourier coefficients will virtually entirely describe the periodic function.

a bandlimited and periodic function can be completely described with a finite set of Fourier coefficients.  also a bandlimited and periodic function can be completely described by sampling a single period with a sufficient number of samples that are spaced closer in time than $\frac{1}{2B}$ where $B$ is the bandlimit.