I've read that in a couple of places.
There are two explanations usually given for why centrifugal juicers lose some of the nutritional value:
- frictional heating, supposedly from the higher speed of the moving parts (although it's never clearly explained where this comes into play, maybe from the juice splatting on the container)
- aeration of the juice (since there's usually more frothing with a centrifugal juicer), which causes the juice to oxidize more and faster.
I'm personally not convinced that either of these is a huge issue, but OTOH I do like the twin-gear masticating juicer we have because it can juice anything and doesn't suffer from those supposed disadvantages of the centrifugal type.
Short answer is no. Vitamins are organic compounds (that is, compounds based on a carbon skeleton) which are pretty small: most of them are formed by 20-30 atoms, not more than that.
Mechanical stress, as well as thermic stress, can indeed interfere with the structure of big organic compounds such as proteins or DNA, which are called macromolecules and are formed by thousands or even millions of atoms connected in complex 3D structures. However, this is not the case for vitamins.
So, in substance, continue to drink your orange juice and you'll be fine!
EDIT: standing what I wrote, it is also interesting to consider that certain vitamins can be enzymatically degraded. This is for instance the case of vitamin C: this article demonstrates how vitamin C degradation could happen when processing broccoli at <60°C, due to the action of an enzyme called vitamin C oxydase. Of course this does not necessarily apply to other vegetables/fruit or to other vitamins.
Personally, I think that the passage of a fruit in a juicer is sufficiently fast that I really doubt there would be enough time for the vitamins to degrade. Would be an interesting experiment to do though.