As we all know, Webster dictionary is all you need to know to pass a bar exam.
In your hypothetical example, the agent doesn't have to say anything.
If Larry Ellison buys 15% of Twitter as a favor to his buddy Musk, he is under no obligation to publicly state anything. All he has to do is to disclose any stake bigger than 5%, as per SEC rules.
Twitter board has no power to question Ellison on his motivation.
They can either trigger the poison pill or not.
If they try to include Musk as part of the poison pill, they'll be sued by Musk and the burden of proof will be on Twitter board to demonstrate that Ellison is in cahoots with Musk.
And when you're in front of a judge and the jury, it's a bit more complicated than "because I said so".