The 18-year-old announced on Twitter yesterday that his mentor had decided to swap his original track for this week's 'love and heartbreak' themed-week.
He jested: "My boss likes to keep me on my feet."
Cocozza added during an appearance on today's edition of This Morning: "Gary thought it would be funny to change my song yesterday. He just didn't think it was working. I trust him."
Barlow switched Cocozza's songs ahead of last week's show as well, snubbing a planned cover of 'You Can't Always Get What You Want' by The Rolling Stones for Ed Sheeran tune 'The A Team'.
Last Sunday, Barlow opted to save Cocozza over rival act James Michael, who was voted out of The X Factor along with Amelia Lily, Jonjo Kerr and 2 Shoes in a quadruple eviction.
Michael told Digital Spy that Barlow made a "mistake" by having him sing the Beatles song 'Ticket To Ride' on the show.