DVDs didn't have that issue, fortunately.

In CDs, the recorded layer is directly under the label, in DVDs it's mid-way through the thickness of the disc so there's a layer of plastic between it and the label. A function of different wavelengths of light used to read them.

Bit rot due to degradation of the organic chemicals in the recording layer is still very much a concern though.

No worries, I had many kind of CD-specific pens back then.