Regardless of where you heard this....
Yes, "movement" can damage a hard drive. Let's define that movement.
Modern laptop HDs are designed with protection against sudden shock and vibration. Go to New Egg or Macsales and look at laptop HD tech specs and you will see the technology I am talking about. Little movements here and there are not going to kill your HD. Drop it from a coffee table to the floor, it may or may not break. Drop it from higher, it will probably break. Regarding movement while use, most laptop HDs are built to withstand 1G of vibration while operating (more or less, depends on brand, model, etc).
By the way, the same goes for your iPod Classic. Don't be paranoid, but don't be careless either.