Your middle paragraph was true, but is now outdated as of the last 15 years or so. This is indeed how the MIT Blackjack Team worked, as documented in books like Bringing Down The House.

However, casinos now know of and how to foil this strategy. The countermove is to prohibit entering a table while a shoe is in progress. Either the new player must wait until the deck reaches its established end point at the cut card, or the deck gets reshuffled immmediately upon the new player entering. Either way, an incoming player can't take advantage of any count.