Personally, I think that it is better to be at a table where everyone is winning and having fun. That woman will lose money in the long run, since she will bust out more often than not when she makes that play.

However, that being said, you are not required to play basic strategy at a blackjack table. If you want to make a play, you should not be concerned with what the other players at the table think. If they don't like the way you are playing, they can leave and find another table.

W mentioned that he would take double down on an 11 in that situation, this is a bad example, since any blackjack player worth his chips would do the same thing. However, he is right in saying that if that player had gotten a 6 (or any card that would have helped the dealer) you wouldn't be complaining about it.

By converse, even playing Basic casino Strategy can burn you. I've seen hands where someone makes a basic strategy play, and ends up burning the table, since the card they got would have led to a dealer bust, for example, hitting a 16 against a dealer 8, recieving a 2, standing, only to see the dealer turn over a 3, then hit for a 10 to get 21. This is the right play, but if the player had stood, everyone would have won. The fact is, that player has no more idea what is coming than you do, and can only make the play that they think is the best at the time. You can let them know what Basic Strategy says, but leave it at that.