Mushrooms grow when their spores are present and the conditions are right. I think providing a picture of what you have would help more in this case to id them.

So the straw factor isn't a factor?

I have no idea how post photos. :( HOWever, we now have a very distinctive bunch growing on the sides since just last night! They're extremely thin, fragile, with jet-black heads at the end of an almost transparent filament-thing.

Does THAT give any clue? Thank you very much.

I don't think straw itself is the definitive factor, no. I have just recently had a similar set of mushrooms grow out of a pile of grassing clippings that I had.

I'm sorry, but I am no mushroom expert. You can upload pictures to a photohosting site like photobucket.com and then provide a link to them here.

Mushroom can grow not only in rice straw but also in woods. I have searched from Google and the link is attached for your reference.

Here is a link that might be useful: edible mushroom grows in woods and straw