On the contrary, you would be demonstrating that, to at least one buyer, it was worth that. By definition.
I think the argument you’re really looking to contradict is this: if 1% of a company is worth $1B to somebody, then somebody would pay $100B for the whole company. That does not follow (and indeed the acquisition price of a company is almost never exactly its “market valuation”).
No.
You are assuming that the money that I buy the sweet shop for is what I evaluate the value of the sweet shop to be worth. That's not necessarily true.
You're also assuming I'm not insane.
If I offer to buy an apple from you for 1 trillion dollars because I believe consuming that specific apple will make me a god, that apple is not actually worth 1 trillion dollars.
> and indeed the acquisition price of a company is almost never exactly its “market valuation”
The acquisition price is almost always significantly more than its market value. The reason is that if you start buying shares on the open market each transaction of yours will raise the stock price, and eventually you will price yourself out of the purchase.
So what buyers do is negotiate directly with the board and propose an inflated price that >50% of shareholders are okay with.