Vibration transfer is identical whether the screw itself is in the wood or an anchor. In reality the screw is still in the wood either way, just fatter with the anchor. It is a myth that the Greedson post screw affects tone. Show me someone who can truly hear the difference and I'll show you Superman's offspring.
The only guitars I have ever had a bridge post problem with (and there were MANY) is Greedson. 99% of the other manufacturers use anchors. I would cringe when a customer walked in with a Les Puke same as I would a Stratocrapper or worse a Telecrapper.
If you are talking about wood density and how it affects tone then yes, it does matter, not the screws/anchors. Wood with a higher density such as hard rock maple absorbs fewer high frequencies where woods with a lower density such as mahogany absorb more. It is not simply opinion, it is science. The higher the density the fewer frequencies are absorbed. "Tonewood" purists are forever arguing the difference between tone woods. What they are actually arguing is the cell density of the media. It doesn't matter if it is yellow, turd brown or fuchsia. More cellulose, more density, brighter tone. Less cellulose, less density, warmer tone.
There are so many points that guitarists argue about such as pickup, string gauge, wood used and even bolt vs set neck. It will never end. Same as tube amp vs modeler. I am not religious on the matter. Show me the science. If empirical evidence proves me wrong I will change my opinion. That's how science works.
Question: Does the AS-50 also have a Bigsby? I have probably replaced more ABR1 saddles than I have owned or serviced guitars and that is in the 1000s.
Here is a great vid that dispels many common misconceptions and superstitions.
https://www.youtube.com/watch?v=n02tImce3AE