Extremely valid point, and I forgot to bring this up: I read the NYP article (god help me), and I could find no evidence of that claim (which surprises me NJ.com cited it for that). In fact, there's even counterevidence within the Post's article:

Some Goya owners have also asked the board to present a motion to remove Unanue as CEO because he’s been using the company to promote his political views, sources said.

“More than 50 percent of the shareholders do not want Bob to be the CEO,” a Goya source said. “All these political statements that Bob is making is dangerous for the company and for us personally as owners,” this person added.

“It will hurt the Unanue name and company if he continues,” a second Goya source and shareholder said. “He should be thrown out as CEO. I think it’s really hurting us.”

In an interview with The Post last week leading up to Friday’s vote, Unanue acknowledged that his job may be on the line.

“I’m attacked by my own family” he said. “I could be fired tomorrow … whatever. It’s touch and go.”

As The Post exclusively reported last year, Unanue narrowly escaped losing his job when he nixed an effort to sell a minority stake in the company to a private equity investor that would have brought in a non-family member CEO for the first time in the company’s 85-year history.

It's still possible that there's some other source describing this alleged restriction, but I don't know of it.