What war other than the bidding war for talent was Jobs threatening?
Google was also trying very hard to build and maintain a coalition of smaller browsers (at the time) that can compete with IE's complete stranglehold on the technical web ecosystem by virtue of its sheer mass. Apple is a notoriously fickle partner in any kind of technical coalition (note how they got bored with other companies dragging their heels on the usb-c standard and released their own standard several years earlier). They had the leverage of both their own browser and their mobile phone platform to position against Google or towards Microsoft if they chose to.
History might have played out very differently if most search traffic from the Apple platform was going through MSN instead of Google.