"The 308 has a bit more pressure than the 7.62 NATO"
This isn't "internet garbage", since it is a fact, and has been long before the existence of the internet.
But, "a bit more pressure" doesn't mean much to most rifles, only to some. And its HOW that pressure is delivered that matters, to those rifles that it does.
Also, HOW you measure the pressure matters. One system can give you much higher or lower numbers than another.
Consider just this, original 7.62NATO (7.62x51mm) specs call for a load that duplicated the 150gr USGI .30-06 loading, approx. 2740fps +/-.
.308 Win 150gr commercial loads run 2820fps (avg - published data in old Gun Digest books and other places) and some makers claim higher velocities, into the 2900fps range.
to get these kinds of numbers (same length barrels) there must be a pressure difference. Generally, its no big deal. In a specific rifle, it might be, but other factors besides just the load pressure play a big part as well.
Rifles like the CETME (HK 91, etc) need a particular level of "hardness" to the brass to work right (along with pressure in the correct range). Gas operated autos depend on port pressure being in the correct range (FOR THEM), and a load's pressure curve, that doesn't matter a bit in a bolt action can be a huge deal in a semi auto.
That box of Remchester ammo is NOT exactly the same as GI Milspec 7.62 NATO in any way other than exterior dimensions. Whether the difference is a matter of importance in your rifle, or mine, is another matter. For most rifles, they are interchangeable and of no practical difference, other than downrange performance.