I'm a Mint user, and I don't think it's safe.
Your data isn't private anymore. That lifehacker article claiming it is safe was written in 2009, before the data security breaches at Sony, Home Depot, Target, Ebay, Apple, Gmail, Facebook, Evernote, J.P. Morgan Chase, Citigroup, the NASDAQ, the European Central Bank, Experian, the Heartland Payment Systems, or the whole long list of healthcare providers that have been compromised. How many examples do you need before you see a pattern?
Pretty much anything you have online is vulnerable. Putting access credentials for so many different financial institution in one place makes that one place an attractive target. I'm sure Mint is doing everything it can to protect that information, but ultimately they cannot possible protect your data and still allow everyone remote access from any public computer.
I think it's only a matter of time before Mint is hacked. On the bright side, I expect Mint to notify me immediately if my investment accounts start emptying out. I'm hopeful they'll be more responsive than anyone on the above list in notifying users of the breach promptly, but given that their entire business model is built on convincing you of their infallible trustworthiness, I suspect they might be more reluctant to admit fault than the average hacker target.