No, you are not paranoid enough.

If there is any concern about fire, the documents should be in a firebox; they are quite cheap, like 19.00 at Walmart/Target.

They are good for about an hour, but will get HOT inside after 30 minutes, so flamables like lighter should not be inside.

I see that LIPO bags are good to "contain" fires, but have never heard of using to "exclude" fires. Interesting idea, but I would not trust with documents.

I do agree that making copies of these documents would be very prudent.