So even if you access another personal e-mail account on your phone S&N will be able to see it. Every little silly thing you do on your phone, they will be able to see. So if you use your phone for Fantasy Football picks, to vote on American Idol, to order condoms on Amazon, to text smutty texts to your married girlfriend, to read and post on Cafepharma... they will be able to see it.
So if you use a seperate personally owned device to access your S&N e-mail, you have to have that In-Tune loaded on your device as well.
I suggest getting a seperate phone or iPad for all personal use. It is a pain because the calendars will not be able to be synced up and you have carry two phones.
S&N says that the corporate privacy policy applies which the employee has some rights to privacy, but I can't remember the details and they don't make it very easy to find or decifer.