I think this has more to do with legals than anything else. Virtually no one reads the page except adversaries who wanna sue the company. I don't remember the last time I looked up the mission statement of a company before purchasing from them.
I sure hope people read the mission statement before donating to a non-profit.
It matters more for non-profits, because your mission statement in your IRS filings is part of how the IRS evaluates if you should keep your non-profit status or not.
I'm on the board of directors for the Python Software Foundation and the board has to pay close attention to our official mission statement when we're making decisions about things the foundation should do.