It's plausible.

Nylon when produced contains plasticizers to make it more flexible: these slowly evaporate out over time (5-10 yrs sounds about right for something of the diameter of a string) so you'd end up with a significantly stiffer material that will support higher overtones and give a brighter sound.

Not sure why black would make a difference: one thought is that the colouring would improve its resistance to UV, so would maintain the molecular structure of the plastic better. Over 10 years or more, micro-cracking of the outer layers of the string from UV damage could tend to produce damping of the sound. I'd be surprised if that was a large enough effect to make a noticeable difference though, compared with normal temperature/humidity variation.