Yes, that's basically what is happening. There's something confusing with my wording (below) of what is happening but here goes:
According to Nyquist, you need to sample at twice the frequency rate of the signal to avoid aliasing.
So, basically you are sampling at 1000 cycles per second (by plotting 1000 points per cycle of the sinosoid)
But if you increase the sinosoid's frequency to 1000 Hz, you need to need to increase the sampling rate (by increasing the number of data points)