For starters, your source probably was referring to a recent study by the UIAA (Union International des Assicociations d'Alpiniusm) on the effect of marking pens on ropes. Permanent markers such as Sharpies contain some acid in the ink, which helps it bond to surfaces. (Interestingly, I have a Sharpie on my desk, and on its side is the inscription,
"Not for use on cloth." A rope sheath might be thought of as a kind of cloth.)
Anyway, the UIAA study showed that ropes can be weakened by the ink. In fact, some ropes showed a 50 percent drop in their ability to absorb energy from a fall. But what this means in practical terms is a different story. Unless you completely saturate the rope with ink, only the sheath is affected. The sheath protects the core of the rope but doesn't add much strength to the rope proper. Moreover, it's the end of the rope that absorbs the most energy in a fall, and the impact of a fall decreases the further from the end (you) one goes. So the theoretically "weakened" segment of your rope is not going to feel anything near the full force of a fallnot unless you're taking a 90' real screamer with no other protection. For rappelling, in theory the mid-point is right at the bend around an anchor, at which point the load is evenly divided into each half of the rope and through the bend. So the marked point can't bear the full weight.
Besides, when did you last hear of a rope breaking due to the force of a fall? Never. Ropes don't breakthey get cut by a sharp edge. Any impact sufficient to break a rope likely would kill you from the sheer deceleration your body absorbed in the seconds before the rope actually snapped.
Worse case for a marked rope according to Scott Newell, who tests ropes for Bluewater: The sheath may blow out a bit prematurely, forcing you to retire the rope. But it's unlikely that the rope is compromised.
Still, I bet that seed of doubt now has been planted, hasn't it?