Elton John has no idea about what's going on with Madonna and Lady Gaga.
Madonna's stance on derivation/emulation/plagiarism is clearly nuanced if you read this article on Confessions on a Dancefloor (2005):
"If I'm going to plagiarise somebody, it might as well be me, right? I feel like I've earned the right to rip myself off. 'Talent borrows, genius steals' [laughs]". She rips off Oscar Wilde while laughing about plagiarising herself and others all over Confessions. Including Boomerang-Referencing Stardust's "Music Sounds Better With You" which references her own "Holiday".
Her sampling of "Born This Way" in her MDNA tour version of "Express Yourself" is a compliment, not an attack. Madonna is too subtle for that kind of thinly-veiled criticism. She is defending Gaga, the same way she defended Kylie Minogue and Britney Spears by wearing T-shirts with their names on her during one of her tours. She was erroneously accused of attacking them, and decided to clarify later.
And there are multiple direct- and Boomerang- references to Lady Gaga in Madonna's "Girl Gone Wild" video. At least five or six. Watch it with irony; Madonna hates smoking and could be accused by a casual observer of glamourising it here.
Lady Gaga herself, before "Born This Way", basically made anyone who would throw Madonna-plagiarism slurs at her look like an idiot with her "Alejandro" video. They both have great senses of humour.
As for Elton John, he's since recovered from losing at the Golden Globes this year to Madonna's "Masterpiece" (which Madonna has since dedicated to Gaga). As Madonna predicted at the time, it would be just another of Elton John's multiple feuds over the years, and that in her experience they would be friends again soon.
Meanwhile Madonna and Lady Gaga are in love with each other's work.