"Everybody is talking about health care - but they don't understand it like Ted Kennedy did."
The use of "like" before an expression with a verb in it is basically accepted now in newspapers, including the N.Y. Times, even though it is not AP Style. It has always been accepted in conversation, in quotes in stories, for veracity ("We didn't play like we wanted to"), and in Peter Frampton songs such as "Do you feel like we do?"
But students need to know that such usage can burn them big time in serious writing. And would it kill anyone to say "as" or "the way"?