Was the nun really the mother?

I haven't seen the movie in a long time but, If I recall correctly, although it is not explicitly said in the movie how much (all of it?) of the stories told by John (Johnny Depp) is fictional and how much is true, it is never questioned whether the nun is really John's mother.

Throughout the entire movie, or at least up until the point where Dr. Mickler (Brando) meets with John's grandmother which tells her prosaic version of the truth about the not so glamorous/adventurous nephews's life, we are led to believe that there indeed might be some truth in the elaborate and fantastic tale told by this delusional kid admitted in the psychiatric hospital after a suicide attempt.

The movie plays on this ambiguity throughout the whole movie, by firstly leaning towards the fable, then towards the (supposed) reality and then, at the end of the film, almost abruptly towards the fable again in the scene where Mickler, his wife and John's reach the mythical island of Eros, where Ana is still waiting for her Juan's return. That is because the whole story is told by unreliable narrators.

Is the final confession of John in front of the commission true (entirely/partially) or is it just a conscious and clever attempt to leave the psychiatric facility? John admits that Dona Ana, the love of his life, was never real, but just a face on a magazine that he fell in love with:

John: So, one day, I was looking at this magazine and there was a centerfold. [...] So, I called up the magazine. [...] One day, I reached this woman who worked there [...] the woman took pity on me and she gave me the girl's number ... so I called her up. I said that we were meant to be together ... and she called me a creep, and then she hung up. I just decided that my life was over ... so I was going to kill myself ... or at least I was going to make people believe that I would kill myself so I could get some attention or something. I never really had any intention of killing myself.

However, this story was previously told by Dr Mickler to John while attempting to establish if John's denial of truth is conscious or not:

Dr. Mickler: I once treated a young man about your age. And he fell in love, oddly enough with a girl on a poster. And ... he tried to contact her. He must have called the magazine a hundred times till finally, somebody at the magazine took pity on him and gave him her number. So he called her and they had a one-minute conversation and she let him know she never wanted to speak to him again. And then what happened? He tried to kill himself is what happened.

Has Dr. Mickler used John's real life story against him in order to give him a reality check or has John used Dr. Mickler's story to look credible and sane in front of the commission and be released?

Ultimately, at the end of the movie, the voiceover of Dr Mickler confesses that:

My name is Don Octavio del Flores. I am the world's greatest psychiatrist. I have cured over a thousand patients. Their faces linger in my memory like summer days but none more so than Don Juan DeMarco. And so it was not so insane that we all found ourselves on an airplane flying to the island of Eros. It was like the Garden before the fall. Everything seemed possible. And how does our fable end? His Dona Ana, his centerfold was she waiting all eternity on the beach for him to return as they had promised each other? Why not? Sadly, I must report that the last patient I ever treated the great lover, Don Juan De Marco suffered from a romanticism which was completely incurable and even worse highly contagious.

What is a fable? The entire story? Or maybe just the end? It is up to the viewers to decide. Just as is up to the viewers to decide whether John's mother has become a nun after her husband was killed in a swordfight in Mexico or because she was struck by guilt and remorse over her cheating on her husband killed in a car crash near Phoenix.

Don Juan De Marco script