Just because you buy a zoom lens doesn't mean it is the only lens you are now allowed to use! And just because you are using a zoom lens doesn't mean you can't still alter the composition of your photographs by using your feet! The advice you have been given is primarily a warning not to stand in one place and stop exploring shooting angles and perspectives just because you have a zoom lens mounted on your camera.

You can still choose to go out shooting some days using only a particular lens such as one of your primes. There are lessons about perspective, field of view, narrow depth of field, framing, and composition that can best be learned by working with a prime lens and having to actively consider the best shooting position to get the shot you envision. The fixed focal length forces you to move to alter the framing of the subject, but that doesn't mean you have to or even should stop moving to alter your composition once you add a zoom lens into the mix.

There are other lessons about perspective, field of view, framing, and composition that can best be learned with a zoom lens. A zoom gives you the opportunity, for example, to explore how the same subject looks in relation to the foreground/background when shot from different distances at different focal lengths using the same framing of the subject. In such an exercise you are zooming with both your feet and your lens in opposite directions and comparing the results!

Can you be a great photographer using only primes or only zooms? Absolutely. But you won't be as well rounded a photographer. Ultimately, I think to be a well rounded photographer you need to have the skill sets to use both prime lenses and zoom lenses in appropriate situations as well as the ability to assess when each is the better choice. Whether shooting with prime or zoom lenses the key is to avoid becoming stuck in a rut (or in one spot) but rather to keep exploring new ways of seeing the world through your viewfinder.