Ok here is a PROOF. It is quite simple, and unlike many other mathematical proofs easy to follow. It's short, and without any formulas. Please ask any question you like.
First of all, we modify the game slightly. When the dealer will draw his cards, he will draw his cards from the bottom of the shoe (instead of drawing from the top). In case there is a cut-card in the shoe, he will draw the cards right in front of the cut card. (But that doesn't really matter - let's ignore any cut card).
Is this the SAME game as before ? Yes, in EVERY aspect. As the shoe is shuffled before, it doesn't matter if he draws from the top, the bottom, or from the middle of an random shoe.
Now, does the decision of a player (say, on third base) hitting his hand or standing alter the way the dealer will make his hand ?.
No it doesn't, because the dealer will draw his cards from the bottom of the shoe, while the player takes the cards from the top of the shoe.
Since the dealer-bottom-drawing and dealer-top-drawing games are identically, the strategy decision of the player at 3rd base does not influence the dealers chance of busting/standing on any number in a normal game.
I leave it for your homework to proof that the dealers chance of busting/standing is also not influenced by the strategy decisions of players at 1st base, and any other base. Tip: expand the argument of bottom-drawing to dealer and all but one player.