I don't know what Swan is arguing there, so I can't enlighten you anymore than he has at this point, but what I can add is this. I get two different readings here. Does anyone else?
Max: "What's the matter?"
[1] Max asked me what was the matter.
=> I was sick and needed to go home.
[2] Max asked me what the matter was (about).
=> It was about a client's missing file.
To me, what can be the object of the preposition
about, in which case the subject is
the matter and the verb
was appears to end the clause, reading [2], or
what can be the subject of the clause, in which case the verb
was sits mid-clause and
the matter functions as a subject complement, reading [1].
There's one more possibility, but it reads awkward, [3]. How does it sit with you?
[3] Max asked me what was the matter (about).
All the best.
