True, but only to the degree that you begin absorbing the float. Anyone who is looking to invest to the tune of BILLIONS of dollars knows that they will very quickly start paying more for each subsequent share they try to purchase from the open market. That's why a takeover offer like this has to be attractive enough to appease a majority of the current shareholders, and done all at once.
I only have a little knowledge of this, so I'm sure more experienced members will laugh and grumble at my description.
With the right slow consistent buying programs, they can fairly quietly buy the stock without causing spikes. Many of the big brokerages likely have programs like that that they offer to their big money customers precisely for that sort of reason. They also would use such low impact programs to sell stocks. The programs have settings, so if someone wants the stock price to receive more of an impact, they can do that. There's only so much the programs can do, though; buying pressure is buying pressure, and same for selling. If anything, I'm guessing the selling programs run slower. I bet they use a lot of selling of options in both directions. A simple example could be sell a weekly put at a strike +$10, start the buying program to target the SP $10 rise over 3 days, and then collect the new shares from the put buyers: let them pay for the stock rise after you already are going to own the shares at a lower price point AFTER your buying program to fill in the non-option obtained shares already ran to bring the price up. Of course, this sets off a bit of a mountain after you have your position. There must be buying programs to prevent that, too. I bet each one does it differently.
They can also go to dark markets, which are another great way to stop big movements from having erratic price movements. The problem there is that I'm sure there's a gossip ring about who is in the dark market, and that gets into a lot of money being made off of retail investors: some traders are ok with that, and some are not. Of course, if it's a dark movement, it may have no impact on stock price at all -- just a weird glitch at 4PM on the tape, or they could even mix tape placement throughout the day.
The word I see being used all the time for the above buying activity is "accumulate".
Or do you think they can't squeeze a $20 billion buy into Tesla's wild swings in price? All an accumulator woud have to do is help the shorts with their FUD campaign for a few months, and while the shorts do their coordinated attack at the end of every day, you can be right there on the other end, accumulating all the way. That fits how Tesla has traded for the last 3 months.