All the answers from Oliver Peters are relevant. I found a solution so simple I wanted to cry when i found it. If you change the video quality of the playback in Avid and put it to Best (The complete green rectangle), the white lines disappear. Simple as that…
The transparency of the PSD isn’t good, I found PNG was the best. 8 bits, RGB color.
I can’t believe I’ve been looking for a solution so simple all that time… Hope it can help someone in the future (7 years later…)