Boyd's move to the Tigers from Peterborough in February very nearly didn't happen after he had undergone a medical at Forest three weeks earlier, but the Championship club cancelled negotiations saying he had failed an eye test.
Alex McLeish was sacked just days after his move collapsed, and the Midlands club rehired Davies.
And the 28-year-old, who used to work in a sweet shop at Hitchin station after being released by Charlton when he was just 16, claims Davies would have rejected him - just like he did during his first spell as Forest boss.
"I'm pretty sure Billy would have had me out if I joined Forest," Scotland international Boyd told The Sun.
"There was clearly something going on behind the scenes. My agent was furious and I was bitterly disappointed.
"But everything happens for a reason and I am now in the Premier League while Forest aren't.
"I have always wanted to play at the highest level and am determined to make the most of it."