Eh, kind of. I agree I could have done a better job. I was trying to quickly summarize this distinction -
A corporation literally cannot exist without a government charter.
Google is able to collect all this surveillance data with impunity due to the state. Google is able to wash its hands of responsibility for the results of its actions due to the state. Google is able to force its workers to be loyal (eg not embezzle for themselves or competitors) due to the state. Google wouldn't have such outsized financial resources without the state printing reams of fiat money.
Heading off the common retort that a private person can do whatever a corporation can do - the relevant issue is scale. It's simply impractical for an individual or a simple group of individuals to scale up to the level of a large corporation.
And yes, this definition does end up catching any corporation as an intrinsic organ of the state. While jarring (because in the US power flows both ways), this is still a fundamental truth. For example if you attempt to set up an LLC or corporation that operates at odds with government policy (eg selling drugs), you'll find out how quickly a corporate veil will be discarded. Actions that are at odds with government policy are defined criminally, and thus all corporate activity is inherently government chartered.
Of course all of this is only useful as a lemma to reach another conclusion. But that's what I was doing - why would Google ever choose to rock the boat? It's not impossible (cf Apple), it's just that there would need to be some explicit incentive for Google beyond mere citizens' hope.