"You want to buy a company so you offer less than it's value, your intent to buy said company now pushes up the price meaning you end up paying more than you would if you had offered a higher price in the first place. I don't get it."
The reality is no one knows exactly what the company is actually worth. The current stock price is just the price of the last buy-sell of shares. You have no idea how much you'd have to offer to get a majority of the shareholders to sell. At one end of the spectrum, some shareholders will never sell, no matter the offer. At the other end of the spectrum, some will sell at the current stock price.
And you can always increase your offer, but you can never reduce it. So if the stock price goes up, after the offer is made, it looks like a majority of the shareholders want more money. So you can increase your offer. It doesn't always work that way. Sometimes, offers bring the stock price down, as everyone realizes that the stock is thinly traded and the current trading price doesn't represent the actual value of the company.
The reality is, that major shareholders will want to make a return per year better than the Dow Jones. So they will hold out for an offer that is better than that. So you'll want to look at when major shareholders bought into Qualcomm, and at what price.