Theory- Prisoners dilemma.

Page is willing to talk. Strzok not needed if she spills. So they have to make it look like she is willing to talk but backs out. Gives him a chance to spill voluntarily- assuming if he does it first on record he will be given the immunity not her. They only need one. His perceived opportunity came when she backed out of testifying. What he doesn’t know is she was going to spill no matter what. This just allowed them to get him in record corroborating.