Ironically, the moment said employee becomes former, Google no longer has claim to any work they do. What's at issue here is the extent of their claims on /current/ employees.
> but anything you think of relating to the company's business belongs to the company.
A company can own /ideas/? Copyrights, yes. Patents, yes. But ideas? Not so much.
Even the idea that the company has a blanket claim to anything you set to keyboard or paper outside of the office seems ludicrous and unenforceable. Write a song? Google owns it. Write a poem? Google's. So why would they essentially get a blanket claim to any program you write?
edit: What's protecting Google's secret ranking algorithms is confidentiality, not copyright.