Another aspect of the "outside" connection that the Psalms provide is the fact that generation upon generation, going back long before Jesus, has sung the Psalms in its own time as a part of its daily prayers. The Psalms are a very tangible connection to the Communion of Saints among whom we walk the Christian path.
I feel supported and comforted to know that my heroes of the faith, including my patron Saints Chad of Lichfield and Joseph the husband of St. Mary took these words daily upon their own lips in prayer to God. In this way, the Psalms contribute to my conception of catholicity. It is as though I stand in an ancient river flowing slowly, steadily, and forcefully to meet me, the water having touched the hands and feet of my sisters and brothers who have gone before and will continue on its course far beyond me.