Nonsense story: The Borgias

Still watching The Borgias and there is a nonsense scene in the 8th episode of the first season.
WARNING - SPOILER!
Cardinale Della Rovere speaks to Gulia Farnese and Lucrezia Borgia about his intentions of deposing the pope. Lucrezia asks: on what grounds? The cardinale says: public lechery. Gulia says: with whom? With you, madame. Either she is completely idiot or...she is idiot.
Even the allegation is nonsense. In the catholic church exists a word: celibacy. It has power. It is a groundstone.  Even basic priests can't have wives (nor kids, obviously). Cardinales? A pope with a wife? With children? With a lover? They built the entire story on a non-existing thing but the other events follow history. Yeah, I know it's fiction. But trying to follow history and building on non-sense things? Too much.
I enjoy the series but the celibacy thing bugs me.
Let me cite some law reference here:
"Celibacy was first written into law for all priests in the 12th century at the First Lateran Council (1123), but it was a common practice much earlier, as shown in the Spanish Council of Elvira (~295-302), which required celibacy of clerics."
And it is 1500 in the series.
Can you tell me what they thought?