Thank you for your comment. But I need to tell you that the analysis I made above is not mine. It is based mostly on the explanation of Prof. Martha Kolln described in her excellent textbook*** (the one that I used when I took linguisgtics). In her book, Prof. Kolln states that "The following modal-like verbs also function as auxiliaries; they are sometimes referred to as semi-auxiliaries.
have to, get, keep
has to, gets, keeps
had to, got, kept
be to, be going to, used to
He has to go.
She got started.
She got to go.
The bus is to leave at noon."
In Doing Grammar****, Max Morenberg seems to agree with Kolln when he states that "Sometimes Gets is the auxiliary in a passive sentence...So sometimes you'll find get as the auxilary in a passive sentence rather than BE, especially in informal language, in order to emphasize the sense of becoming.
In addition, here is one of the definitions of get I found in a dictionary.
(used as an auxiliary verb fol. by a past participle to form the passive): to get married; to get elected; to get hit by a car
(Random House Webster's Unabridge Dictionary)
I completely understand what you explained above. To me, it seems like this partial auxiliary property of "get" is still controversial, and it's a bit unfair to claim the opposing view a mistake.
***Understanding English Grammar, Martha Kolln, Macmillan
****Doing Grammar, Max Morenberg, Oxford