How to misunderstand the Coase theorem

This comes from Matthew E. Kahn's Environmental and Urban Economics blog:

My fellow University of Chicago economists, stop reading Krugman's latest and explain this puzzle to me. A United Flight to Denver was diverted to Chicago because of a fight between two 48 year olds over whether the person sitting in front in Economy Plus has the right to recline her chair. For details read this.

As we get ready to start the new academic year, here is an excellent example of the Coase Theorem not working! Who has property rights on an airplane when the person in front of you wants to recline while you care about your knees? Why was this United flight diverted to Chicago? Wasn't that a destruction of resources for everyone involved? My fellow Becker students, what is the answer? You have 10 minutes to answer this 6 point question. The Coase Theorem predicts that the recliner should have paid the person behind her? True, false, uncertain. Explain.

Kahn states "here is an excellent example of the Coase Theorem not working" and then asks "Who has property rights on an airplane when the person in front of you wants to recline while you care about your knees?" And he does not seem to notice the importance of the second point to his first point.

The Coase Theorem assumes that property rights are well defined, it doesn't matter who has those rights, but someone must have them allocated to them. The problem with the seat example, as the second point makes clear, it that property rights are not well defined and thus the theorem does not apply here. Not, at least, until the airline clearly defines seating rights.