A turing machine is the mathematical representation of today's computers. Originally, Alan Turing proposed a method to test a machine for artificial intelligence. The test boils down to whether or not a machine could pass as a human (see http://en.wikipedia.org/wiki/Turing_test for an explanation of the test). Today, however, the meaning has been warped slightly.
Originally the turing test was performed on machines. Now, (colloquia it seems) when a PERSON fails the turing test it means that person would be mistaken for an A.I. bot. It essence (at least in my opinion) he saying that the managers comment demonstrates the lack of intelligence needed to pass for a human. He's acting as a programmed (business school brainwashed) bot. There are perhaps a few other interpretations of it as well. If anyone else has any other insights they would like to share I'd love to read them as well.
Disclaimer - I love business schools they teach essential concepts... but sometimes the people that come out of them think they know everything and never really learn to think :)