First of all, it's just good sense always to carry a compass. (A real one, I mean; yes, your inner compass is vital, too).
Second, that compass isn't going to do you any good unless you trust it.
If you've ever gone deep woods hiking, then you know how much your life depends on this advice. For some reason, as soon as we get lost, our *inner* compass is very much convinced that the little metal tool in our hands is absolutely wrong--that there must be some kind of rogue mineral deposit on this VERY SPOT to make it go so haywire.
Follow the inner compass in spite of the real one, and you'll be lost for a very long time. But if you keep setting and heading toward landmarks by the real compass (the earth-pole-guided/non-subjective one), you'll feel off, but you'll get on course. It's disorienting and a test of faith. But I'll tell you this--you'll never doubt again.
So, no. You don't need the whole picture. You don't even need a map of the part of the picture you've got. What you do need is a compass to verify that, despite your orienteering skills, you are indeed headed in the right direction.