Blurred Lines

Do infants and high-end dining cross an imaginary line? Well it seems that, that exact line has been crossed at Michelin rated (3 stars to be exact) Chicago A-list eatery, Alinea (pre-fixed meals run at about $200, and are pre-purchased.) Although not right, it may be one thing for fellow patrons to gawk and make side-eyes at the situation. However, what happens when the establishments head chef tweets about the situation?! Is that imaginary line completely thrown out, abandoned and a new level of inappropriate then reached?
So, who's right and who's rude? Should parents not be allowed to bring children into restaurants or public places with a high ticket value, where others can be disrupted? Should establishments be able to deny entrance when adults are accompanied by minors?
Whether imaginary or not, clearly a line has been crossed, but on who's side?