So basically what you are saying is that it is only possible for a single hasher to solve a block if it is just their shares that solve the entire block.
That would imply that a solo mining pool is a fraud as this will NEVER realistically happen with the hashing power in the hands of home miners.
It would most certainly not imply that a solo mining pool is a fraud. I'm not sure how you drew that conclusion from this discussion. Is it likely that I will solo mine a block of BTC? Nope. Is it likely I will win the powerball on Wednesday? Nope. Doesn't mean I won't pick up a ticket for a couple bucks and try anyway.
EDIT: It is not a combined effort of shares that solve a block. It is a SINGLE share that does it. Each time you're attempting to find the solution, it either works or it doesn't. Flip a coin. Either it lands on heads or it lands on tails. It can't land on both at the same time. Each flip of that coin has absolutely no relation to the flips before it, or the flips that come after it.