This happens with most guitars. It's always the "g" string when doing a D cowboy chord. It's worse on thick fretted guitars (and PRS frets are relatively thick) but in my case at least, it's not the nut, and it's not the intonation. The string is just stretching when you push it down to the fret board. You can verify this by only pushing the string as far as you need to in order for it to make contact with the fret. You'll find, I think, that it's in tune at that point. That's not how you'd play it in real life of course, so I always tune by ear, with the G string tuned as a compromise. As to why it's the g string, and why it's only when low on the fretboard, it's just the geometry of the frets and relief I think. It happens with all of the strings actually down low on the fretboard, but it's always worse with the G string.
If you do the experiment, putting only enough pressure on the G string at the second fret so that it makes contact with the fret, then pluck the string, then push down all of the way to the fret board, you'll hear it clearly going sharp. You can either change your playing style or compromise your tuning (and it doesn't require so much of a compromise that it's noticeably off elsewhere.) Or get thinner frets...... I'm not saying that cutting the nut down won't help at all...but that it won't completely solve the issue.