Being paid directly for a service by a company (Google paying for the privilege of being the default) is to be directly funded by that company. You're right that it's not the only source of revenue, but it's absolutely a direct source of funding.
That's still "just" a B2B relation and not "that one company is funding is".
Now, I'm not arguing about how good this situation is (it's bad, for a startup it's actually worse) just that it's not "funding".
Mitchell got Google to pay nearly double what Yahoo was willing to pay and has gotten Google to pay more each year for a dwindling user base.
If someone was going to Walmart and paying millions for a box of crackers, you’d be right in assuming the transaction wasn’t about the crackers.
They owe you a box of crackers. Once you've departed with it, they're no longer beholden to you.