I am not an expert on this question, but I have never heard this before.
I believe both 7.63mm NATO and GI .30-'06 have very nearly identical internal ballistics.
IIRC, the current-day manufacturers of "Tanker" Garands offer them in both 7.62mm and .30-'06. Can't see them doing that if there were known ammo issues.
Other than 7.62mm being marginally more accurate, and much less expensive to shoot than .30-'06, I don't know of any innate drawbacks to a .30-'06 "Tanker" Garand conversion, properly executed.
If the rifle was to be used tactically, a flash-suppressor on the shortened barrel would be a valuable, perhaps life-saving addition.
Now, then, if the conversion was improperly done, or mis-loaded ammo used, thus resulting in an overpressure condition, a very dangerous situation could develop.
Leaving aside the unlikely scenario of an action or barrel bursting (at least a forged, GI action), an overpressure situation could result in the op-rod being slammed back with sufficient force to break it.
This would probably kill a left-handed shooter, but most likely only blind a rightie who could still carry on with his/her left eye.
This is important!
Every Garand shooter should verify that their op-rod has received a relief cut at the juncture of the op-rod handle and the projection from the op-rod body. It's about a 3/16" dia. cut, and if it's there, you'll have no trouble seeing it. Original, so-called "un-cut" op rods are valuable collectors' items, and also can be dangerous to shoot!
After a few rifles malfunctioned, the military established a requirement that all old and new manufacture op-rods receive the stress-relief cut. The cut is mil-spec, period.
If you have an un-cut op-rod, don't shoot with it! Once the rod cracks, it not only becomes dangerous, but also worthless.
Either use it to restore a collectible rifle, or sell it for a lot more than a NIW, cut op-rod will cost you.