When the vinyl is cut from a digital master the engineer must TONE THIS
DIGITAL MASTER LOUDNESS FACTOR DOWN. He/she has no choice on this
because of actual physical limitations with the cut grooves on the
record, and noise itself.
This statement does not sound right. We've yet to encounter a digital master file that we had to 'tone down'; what you are dealing with here is simply that you have to find the right level to get everything in the groove (so this could be simple semantics), but IME you don't have to limit or compress the signal going into the grooves to do that. You don't have to limit the bass either. You do have to be on the lookout for out of phase bass, which can occur in multi-tracked recordings; this can be dealt with by a passive process that senses the out-of-phase bass and makes it mono below a certain frequency for a few milliseconds. But if you are careful and spend some time with the recording, quite often even that process can be avoided simply by changing the groove depth and perhaps adjusting the overall level by a db or so. One or 2 db can have a huge effect when mastering an LP; -3 db means half as much power in the cutterhead- half as much excursion. So reducing the level by only a db might be all that is needed to make the project work, and in the end result that db is hardly audible.
It really comes down to production- if the producer is smart they won't send the LP mastering house the same file that was used to master the CD (which often has limiting, EQ and compression), instead they will send the master digital file with the understanding that the LP mastering engineer will deal with it as needed.
But in all cases the LP is being mastered with something very much like the master digital file, whereas the CD likely is not. Further, people do still master with analog tape, which is great when it happens. This is why the LP usually sounds better- its closer to the source if nothing else.