Is the blackjack strategy in Beat the Dealer incorrect now? For example it says to double on A,2 and A,3 against a 4, but on the set of rules at http://www.blackjackinfo.com/bjbse.php it says that you should Hit??
Beat the dealer is correct and so is the strategy trainer. Beat the dealer is for single deck and the chart you were looking at is for 6 decks. I don't know if you are aware or not but basic strategy can change depending on the number of decks or rules. You should always try to play the correct strategy for the game you are playing.
While this is true, there are several composite strategies, that give up very little and work for SD DD 4D 6D and 8D H17/S17, DAS/nDAS without modification. While SystemsTrader is correct, your motivation (and expectations) and playing conditions may alter whether you learn 1 composite strategy, or perhaps 2-3 specific ones.