Seed Saving: Why is storing seeds in plastic bad for them?

I spent last Saturday morning cleaning, sorting, and storing about twenty different neighbourhood and park-collected seeds with the help of some materiel liberated from my last employer, including some handy dandy 50mL polypropylene conical tubes.

I learned today that I can store seeds in paper or glass containers, but never plastic. I haven't been able to find any justification for this, other than that plastic containers will encourage the growth of mold thanks to the lack of air circulation and the moisture from the seeds. But wouldn't this also be a problem in a glass container or, for that matter, those foil envelopes that retail seed is sold in?

The day before yesterday, I received a shipment of seeds from the lovely folks at Seeds & More, all in little plastic ziploc baggies. Should I transfer them immediately into something else before they're ruined forever?

So, Interwebs, I ask you: are my seeds doomed to fail if they're stored for several months in my polyprop tubes, and if so, why? What's the ideal storage container?