Well I've found a similar concept in the the gospel of Matthew. In fact, this might be where the song comes from. Here are the verses from Matthew 6:
4 so that your giving will be in secret; and your Father who sees what is done in secret will reward you.These verses seem to show that God is somehow especially present in secret places or when there are secret acts of righteousness offered up to him in worship. We know that God is everywhere all the time, but these verses say that he not only has a special blessing of his presence in the secret place, but they (technically just verses 6 and 18) say that the Father "is in secret." I don't think it's trying to stress anything too literally, but I do think it's meant to cause us to want to go to our closets of prayer and fasting and meet him there. There is reward there.
6 "But you, when you pray, go into your inner room, close your door and pray to your Father who is in secret, and your Father who sees what is done in secret will reward you.
18 so that your fasting will not be noticed by men, but by your Father who is in secret; and your Father who sees what is done in secret will reward you.
That was enough to encourage me, but more thoughts have followed. Tragic ones.
Not only do men in their own self-righteousness and God-despising attitudes forsake God's blessing for the notice and praise of man (see context), they actually turn places of secrecy which are intended to be sanctuaries for acts of pure and holy worship into unholy abodes. They take a secret place and use it for lust and immorality. They take a solitary place and use it to stew with bitterness and hatred for fellow man. What's deep in their heart comes out when they are alone, and the very place that God offers a special blessing of his presence and an opportunity to seek the notice and reward of God, they defile.
God help us.