I've always supposed this phrase derives from Acts of Contrition, as recited by penitent sinners after confession. See, for example, the several forms given near the end of rc.net's Confession page, somewhat as follows:
Oh, my God, I am heartily sorry for my sins. Because I dread the loss of heaven and the pains of hell, but most of all because they offend Thee [...] I firmly resolve, with the help of Thy grace to confess my sins, to do penance and to avoid the near occasions of sin.
That is, for my sins may be used to suggest (sometimes humorously) that what someone is doing or going to do is a sort of penance.
In the example quoted in the question, it's possible the phrase is being misused, if the speaker does not mean to imply that what they are doing is a penance, but rather a sin in itself.
However, if they have in the past used shady sources, it may be saying they are now required to used the national news sources mentioned.