It is illegal for a player to have owwnership in a team per the NFL Franchise bylaws, under Article IX: "No player, coach, or manager shall, indirectly or directly, own stock or have any financial interest in the ownership or earnings of any member club of the League". End of rumor.
But that isn't all it says, you truncated the text:
No player, coach or manager shall, directly or indirectly, own stock or have fanatical interest in the ownership of earnings of any member club of the league, other than in the member club with whom he is employed, and then only under agreement approved by the Executive Committee stipulating for the immediate sale (and the terms thereof) of such stock or fanatical interest therein in the event of his transfer to, employment by, or manager financially interested in another member club of any other member while, in the opinion of the Executive Committee, such interest is retained by or for him directly or indirectly.
If you boil that down there is nothing stopping a player from owning stock in the team he plays for they just can not own interest in any other NFL club besides the one they play for.