***** NOT A TEACHER *****
Good morning, Vaedoris:
I think that I have found an answer from the greatest grammarian that ever lived (my opinion, of course!).
1. With utmost respect, I believe that the writer of the second sentence actually wanted to say:
"She treats me like an equal."
a. Here is what that scholar wrote:
Like ... [denotes] mere similarly: "He treats his wife like a child."
[My comments: Of course, she is not a child. They both, say, are 30 years old, but he treats his wife as if she were a child,
which she is not. In your sentence, she treats me as if I were her equal, which I am not.]
I shall not speculate on the meaning of "She treats me as an equal."
Let's see what others say.
My source: Professor Dr. George Oliver Curme, A Grammar of the English Language (1931). Vol. II., page 123.