IIRC, the website the notice was added to was specifically a the site of law firm that Google had contracted with regards to the ongoing concerns of unionization. It seems like there's a fair argument to be made that it was related to the site, although there are arguments against that as well.

But in that case, the notice would fall out of scope of the plugin - which is to notify Google employees of the relevant laws or company policies about the use of a site. This would be about the generic right to unionize, which wouldn't relate to that site specifically. What actions would a user be taking on that site in that capacity, especially if that firm is representing the opposition?

She was reminding management (who are also employees) that anti-union stuff is illegal?

Not all anti-union stuff is illegal. Hiring a law firm to consult on employee management and unionization would not be illegal. If anything, they should be learning the correct and legal actions that they can take based on the consultant's recommendations.

Not to mention, the comment the plugin displayed wasn't saying anything against illegal actions, but rather stating that concerted activities are protected. I don't see how that has any bearing on the use of a law firm's website.