Obviously, it is difficult to know with certainty if the "bitcoinEater" address is really one for which no one knows the private key.
It's impossible to know with certainty, but you can
easily be certain there's no such owner. Same as with PoW. You can't know with certainty that one spent millions of dollars to find a valid hash, but you can easily assume it's true, and you'll be right. One ought to spend millions, on average, to accomplish that.
It's realistically impossible to find a valid Proof-of-Work without the work.