Did only Levites leave Egypt?

Richard Elliot Freedman has a new book on the way in which he argues that only Levites left Egypt. He says that they were the ones who experienced slavery and knew of the God called YKVK. After migrating into Israel they shared these teachings with the loosely related tribes who were already there and gradually, over time, it became part of the Israelite sensibility.  

The main point in favor of this argument is that only Levites and Levites agenda items (like the temple) are mentioned in the Song of the Sea, which is widely considered to be the oldest (or second oldest) part of the Bible. Meanwhile, Levites and their agenda items are not mentioned in Deborah's Song, also widely considered to be the oldest (or second oldest) part of the Bible. He suggests that each song dates to a time before the Israelite tribes and the Levites encountered one another.

The part of this that is thrilling is that it represents the first critical argument in support of an Exodus experience (that I know about) . Instead of reminding us that no real evidence exist for the Exodus and that there is no conceivable way that so many people could have moved through the desert,  here is a noted scholar and critic arguing that at least some of our forefathers did escape Egypt.