According to the Scottish Social Attitudes Survey (PDF), 32% of Scots agree that "the UK government should make decisions about defence and foreign affairs; the Scottish Parliament should decide everything else".
To a naïve observer, that sounds like many Scots aren't too happy with Westminster's social spending policies, but that they think their foreign-policy interests are handled well by the government in London.
However, very few Scots seem to love Trident (located very close to Glasgow), and most think the Iraq war was a disaster. Scots in general don't seem to get excited by the thought of defending the Falklands, either. Furthermore, the instinctive hatred of the EU so common in England is quite unknown in Scotland.
In other words, it seems to me that Scots disagree more with the Westminster consensus with regard to defence and foreign affairs, not less. So why on Earth would a third of Scots want to retain these links?
Could it be that what they actually want is independence with a lifeline? Basically this group of Scots might desire full independence, but they don't trust themselves and their compatriots not to make a mess of it, so they want the UK to stand ready to save them, in the same way a young adult can move back home with their parents if living alone doesn't live up to expectations.
I guess that all these devo-max supporters really want is a guarantee by Westminster than the UK can always be recreated at Scotland's behest. Of course London will never say this, because such a guarantee would be the surest way to ensure a Yes in September.
What we need to do instead is to reassure these voters that Scotland is in a better position than probably any other non-sovereign nation to be a successful independent country, and that an independent Scotland will thus never ever want to recreate the UK. We won't need that lifeline.