"Biasing circuit"??? The GFCI has a toroid transformer core with both power leads are wound through. There is also a sense winding. As long as the current in the power leads is balanced, there is no net flux and no current in the sense line. When unbalanced, a current is generated in the sense line which is detected and used to trip a relay.
There is no biasing.
I know learning about stuff is not your strong point. Your "go to" approach is to invent ideas of how things work, rather than doing some research and learning. I especially like that you used Google to find some electrician who shares your erroneous beliefs. "don’t play well together" That's the sort of professional language I like to hear.
Unfortunately, I can't find any info on this from anyone who knows what they are talking about.