Many of these 'old wives tales' began back before modern materials were manufactured. Therefore, I think that they may have been accurate at one time, but perhaps aren't any longer, as we've change the chemistry so much.
I do believe that fabrics need to breathe, as I've seen dry-rot and molds myself plenty of times on a wide variety of things, not just fabrics. Coming from TX, were there is a constant high humidity and very high heat, this may be our contributing factor (remember, it even gets in our walls here, if not cared for).
If you haven't had a problem to date, you probably won't. But, it's a choice that we each have to make - whether to believe these tales are viable in today's market, or not. And whether we're willing to take a chance :)
Debbie in Austin
P.S. Reminds me of the tale of sun fading...it can happen if you have older windows, and most are wise to avoid it, but since I have the 'newfangled' energy windows that don't let in those harmful rays, I've never seen any fading of my fabrics, threads, carpets or draperies...so it doesn't concern me in the least.