Unfortunately there is no permanent downloads via simply URL. Sometimes happens, sometimes not
Looks like firefox generate specific messages in some situations (in my case it's >90% new banner window) that flashgot treats as "start downloading".
OS is WinXP+SP3. Will try also check on Win7 and also find out more precisely in which situations it happens. From your side you can do log more
detailed . Have feeling that it begin to happen since firefox 4.0.1 but cannot exactly remember when it happens firstly.
Mozilla/5.0 (Windows NT 5.1; rv:2.0.1) Gecko/20100101 Firefox/4.0.1