Add this to the list of things you're "sure" about, but shouldn't be.
Nowhere in the EULA for Microsoft Office (their most profitable product) do I find text requiring you to run it on Microsoft Windows. I read it top-to-bottom, then searched for "Windows" (which never occurs) and then "operating system" (which occurs only to warn you that they use your operating system to get to the Internet).
This is correct on the face of it. However, some of the terms, though vague, effectively prohibit running Office under Wine, etc. The following phrase occurs in the Office 2007 EULA: "...In doing so, you must comply with any technical limitations in the software that only allow you to use it in certain ways." The phrase "...technical limitations..." is present four times in total; particularly combined with some of the license verification verbage certainly could be used in legal arguments as rbanffy suggested
You are right about Office 2007 (the one license I found), but you are wrong about Internet Explorer. It's license states clearly you can only use IE if you have a license for Windows XP, Vista, Server 2003 or 2008 (the IE8 on my wife's corporate notebook has a Brazilian license that doesn't mention Windows 7)