They can always do that, by just issuing more shares. In fact, if you buy X shares, the percentage of the company you own could well decline over time. Or increase, in the case of stock buybacks.
If you've ever wondered why corporations have authorized and issued shares, there you go. Increasing the authorized share count requires a shareholder vote. Issuing shares under that cap does not. When shareholders increase the number of authorized shares, they are delegating that decision making to the Board.
It wasn't always like this. But as finance sped up, particularly towards the end of the 19th century, a railroad company which had to hold a shareholder vote to raise emergency equity because their free banking deposits in Nevada went bust would find itself systematically outmaneuvered by the ones who had pre-approval to plug the hole. As a result, most corporations now authorize the maximum number of shares reasonably possible, in almost all cases only moderated by some states' franchise taxes varying by number of shares.
So far I've tried to understand the poison pill and there aren't any satisfactory responses, either on HN or elsewhere in the news.
Wikipedia of Shareholder's Rights Plan is skimp in details as well.
Everything I hear ostensibly appears to be "That should be illegal, makes zero sense". So with no good information out there, it seems like no one is an expert at this and making up bullshit.
I'm interested in this assumption that because you do not understand something, no one else must either. Is this a heuristic you apply to all fields of knowledge, or just business law?