First off, you can get a different answer from the IRS every time you call--the accuracy of their "help desk" is stunningly sub-par. As a former attorney and the spouse responsible for all our financial affairs (including and especially taxes) I've been researching this one for a couple of years now, well before we even assembled and submitted my PR app. Citizens of the US are generally required to file US returns. If he has no income to declare, he's not required to file, but remember that unemployment benefits, bank interest, etc. all count as "income." We will continue to file US returns, just to stay on the safe side.
I stumbled across this blog on the subject. Don't know who maintains it, but he's assembled a lot of reports and articles from reputable sources (Financial Times, Financial Post, CPA websites, etc.) Read only when you don't already have a headache:
http://usxcanada.wordpress.com/start-here/