Artificer,
Resting the rifle near the muzzle doesn't "induce vibrations", the vibrations are induced from the trigger, lock, cap/primer (if applicable) main charge burn and movement of the projectile down the bore. The vibrations run through the whole gun just like waves in a pan of water so vibrations induces by the lock reach the muzzle long before the projectile even starts moving and it may force the barrel above or below the nominal plane established with the barrel at assumed rest (yes, "assumed" because as stated before, everything in the environment that is above theoretical "absolute zero", 0° Kelvin/Rankine or -459.67°F, does induce some level of vibration/movement in everything. In the real world, thermal energy induction and differentials caused by sunlight, breezes and the stock should never be discounted as they are the most likely environmental conditions to cause accuracy problems within the gun.)
Back to the point - any time you place a gun on a rest be it mechanical or human, you're inserting fulcrum points. As the vibrations and annular pressure waves pass through the length of the gun, they're going to interact with the fulcrum points and how they react depends upon the conditions of each individual shot fired. No two rounds, no matter how carefully prepared, are ever "identical", close but not exactly the same other than by pure random chance.
As it relates to how you rest or hold a long rifle or modern rifle, the actions and reactions related to vibration and annular pressure waves follows the same lines. The more the stock interacts with the barrel, the more variables you're adding into the equation and removing as many variables as possible was my focus during the development of Ultra-RVC. Just as taking a barreled action from the stock and placing it in a machine rest can completely change the level of accuracy, it does little more than prove that mechanical interaction with the stock is very much real and thus the more the stock can be isolated from the action and barrel, the less negative affect it has.
On a full-stock, and especially a long rifle, the variables of the equation are increased exponentially purely in relation to the length of both barrel and stock. If we look back in history, many of the shooters using cross-sticks did so with a leather sling joining sticks and being the only thing in direct contact with the rifle - the same applies to what became known as the Creedmoor style of resting the stock/barrel between the instep and ankle as opposed to using a more solid rest; whether or not it was known at the time remains debatable but in effect the purpose of both methods was to help reduce the amount of vibrations being reflected back into the gun by using a rest that absorbs vibration and annular pressure waves.
The second point that is primary to long rifles are how the annular pressure waves affect accuracy because the barrels are normally pinned to the stock in multiple places throughout the length of the barrel. When the annular pressure waves traverse the barrel, the stock is playing a key roll in the resultant outcome of how much and to what direction/angle the muzzle moves.
Third condition that is primarily associated with a long rifle is the actual barrel length itself. Even a "hot load" pushing a PRB well in excess of 2,000 fps still has the ball in the barrel for a long time which, of course, gives the barrel all that much more time to move around before the ball exits. On the other hand, the fact cannot be disputed that the PRB has considerable advantages over conical bullets because of its extremely small bearing surface and the nature of the patch to respond to the changes in the bore diameter caused by the annular pressure waves. However, the affects of annular pressure waves on have on changing the plane of the muzzle before the ball exits cannot be discounted nor can the fact that the much lower frequency produced by black powder brings the vibration frequency created by the main charge much closer to the frequency of the annular pressure waves which means they do have a higher probability of combining to create radical changes in the muzzle plane which is why you'll hear people often complain about "that one d--- flier!" that has no other plausible explanation.
How it relates to ML's is that I've bedded several half & full-stock rifles and pistols with my flexible compound with very good results. A full-stock I had, .40 swamped percussion, refused to shoot acceptable groups bench or free hand, after bedding the groups were more than acceptable and it didn't care if it was a sand bag or human hand under the forearm but nothing is a cure-all especially if there are other issues going on.