1.) Different passages must be so interpreted, if they can be, as not to contradict each other.
(2.) Language is to be interpreted according to the subject matter of discourse.
(3.) Respect is always to be had to the general scope and design of the speaker or writer with attention to historical/cultural influences.
(4.) Texts that are consistent with either theory, prove neither.
(5.) Language is to be so interpreted, if it can be, as not to conflict with sound philosophy, matters of fact, the nature of things, or immutable justice.
I will start my personal presentation in light of the OP with the following remarks in light of rule three (3) of the Rules of Biblical Interpretation listed above that I have chosen to follow.
(3) In dealing with the historical /cultural issue of interpretation, I can see nothing more enlightening and helpful in understanding this passage than the fact Alfred Edersheim, one of the most well know renown scholars on Jewish social life and history, amplifies for the reader. In his book “The Life and Times of Jesus Christ the Messiah” he writes, “So far as their opinions can be gathered from their writings, the great doctrines of Original Sin, and of the sinfulness of our whole nature, were not held by the ancient Rabbis.” In his foot note he states, This is the view expressed by all Jewish dogmatic writers. See also Weber, Alstsynag. Theol. P. 217
In another place in the same book, he states that “the doctrine of hereditary guilt and sin, through the fall of Adam, and of the consequent entire and helpless corruption of our nature, is entirely unknown to Rabbinical Judaism.”
This I believe helps us establish the historical and cultural setting in which the writer, David, being a Jew, lived. It helps us establish clearly the framework that surrounded and molded the theological notions that he would or did espouse, original sin or constitutional depravity not even a remote possibility, for to do so would have went absolutely counter to the established views of the very leaders and Rabbis of that day. Due to these clear facts presented by Alfred Edersheim, I believe it is all but impossible to believe that David, a Jew, would be establishing in any way a doctrine or dogma that would be at antipodes with that which we know was completely outside of the framework of Jewish thought in the day preceding, present, or subsequent to the time this Psalm was penned within the corpus of Jewish thought and belief.
I conclude that one notion this passage cannot be establishing is the notion of original sin due to the fair examination of the historical/cultural evidence I believe is valid. Whatever this verse is establishing must of necessity, according to this evidence, be something other than the establishment or acceptance of the dogma of original sin.