I would give my password to MSN support if they needed it to solve a problem that's bugging me a lot. But since they don't actually need your password but only your permission to acccess your account
Support changed my account settings a while back, with my permission. Nothing dodgy about it. True they didn't go into my actual email account but what do you think would happen if a microsoft helpdesk employer would "steal" accounts from their customers and the news got out? Honestly, they're just doing their job and if you are sure that the email is in fact from support and not something else, go for it and get them to solve your problem.