I’m not assuming anything. Cardinal Dolan and Fr. Thomas Rosica both said the Pope never went into a private room. Msgr. Dario Viganò says otherwise.
Yeah, sure you're not. Read what you yourself posted again.
The accounts related by Cardinal Dolan (as later confirmed by Fr Rosica) and Msgr Vigano do not conflict.
From the article you posted "The newly elected pope never left the Sistine Chapel for a period of reflection before finally accepting the papacy," Rosica said. Note, this is also what Dolan said (link to what he recounted is also in your post). Emphasis added.
Also from the article you posted, Viganò was inside the Vatican in the moments immediately after Francis' election and before the new pope stepped out to greet the world. He says when Francis left the Sistine Chapel to walk toward the balcony, he had his eyes down, he wasn't smiling, he didn't say anything to the cardinals, and was as if he were carrying "an enormous burden."
Then, however, Francis stepped into the Pauline Chapel, where a throne had been set up for him to use for prayer. Instead, Francis asked the two cardinals walking with him, Jean-Louis Tauran (who made the "Habemus papam" announcement) and Agostino Vallini (the vicar of Rome) to sit with him in the chapel's back pew.
Again, from the article you posted and emphasis added.
No one is lying. This is all stemming from confusion resulting from sloppy reporting (at least that, if not more) on the part of the atheist at La Repubblica.