This is not completely accurate. It's not wrong per-say, but not complete either. The whole answer will take a little to explain so...here goes:
Once a sighting device is adjusted to the particular gun it's on, any movement will affect future accuracy. The question then becomes, what kind of accuracy are you concerned about?
If you remove the optic, but don't move it in the rings, it should be close when re-installed. However, nothing is perfect and it will be a little different than before. How different will depend on a few variables; how good are the rings, and how consistent will your upper allow them to be?
For example, EOTech says their quick disconnect mounts are +/-1MOA upon remounting. This means that when you zero the optic so that it's perfect at 100 yards, when you remove and replace the optic, the point of impact (POI) will be the same as before it was removed, but could be as much as 1" away from where it was zeroed before. So, if it were dead on and you remove and replace the optic and now it's hitting 1" high, it's still within spec.
This leads to, what kind of precision do you expect from your gun? If you're happy with 2MOA, then removing and replacing your scope, as long as you don't futz with the rings, will not be an issue as long as you have a quality set of rings. (Hint: UTG does not make quality rings, but they work if you don't move them.) However, if you want the best accuracy you can milk out of your gun, don't ever move the optic once you've zeroed it.
Also, there are several factors affecting accuracy of your rifle. Quality of the sighting device, quality of the bore, quality of ammo, condition of the bore, quality of the chamber, trigger, skill of the shooter, type of rest...and the list goes on. All these things affect accuracy. If you want the best repeatability you can get, don't remove your optic once zeroed.