As it eventually explains, Balducci is an official of the Italian government, not the Vatican. (IOW, he's not a priest, not the Pope's right hand man, doesn't tuck him in at night, etc., etc., etc.)
He holds an honorific title as a "Gentleman of His Holiness," which the article describes as a "ceremonial usher".
I don't think the "Vatican chorister" is a priest, either. He's a singer.
To put it in terms that a British audience would understand, it's as though someone the Queen had knighted was consorting with a minor employee of Buckingham palace to procure homosexual partners.
"Palace, Queen Rocked By Gay Sex Scandal" ... no, somehow I can't see it. Only if the Pope is involved somehow.
It is probably all that you say - but what a strange place to contact your own procurer unless he is a well know go-to guy among the cognoscenti for that sort of thing.
From the article:
A chorister is usually a 'boy' singer...