They really ought to have a different policy based on the significance of the page on their site. Isn't a page with 40,000 likes worth requiring the complainant to provide some documentation about their infringed trademark? Sure, someone complains about a band with 1500 friends, take it down and let them battle it out. But a company with 40,000 users on your website ought to be treated with a little discretion. The number of times that companies with that many fans are the cause of a dispute cannot be so overwhelming that they can't do a tiny bit more due diligence.