It is a lot safer to shoot a 308 in a NATO chamber than the other way around. This is mostly because the tolerances of the 7.62x51 case is more generous than the 308 SAAMI specifications. In some of those circumstances you can have pressure spikes.

There is probably a lower risk than what is projected around the internet but why risk if you don't have to. It reminds me of the debate about using a case to set head space. If you know what your doing and you reload it is no big deal. But if you know what your doing, why use a case?