No, its 'refining' if its third party ore if someone else is doing the mining. Important distinction.
The below is a really old article (pre expansion of many of these companies) and it shows how many refiners are already in existence and producing much higher numbers than continually quoted here. You can get more recent figures on the numbers they are punching out if you research company by company.
Does it mean the claims of top 5 or 10 producer are false? Absolutely.
Does that mean this company strategy cant work? No absolutely not. Dont need to be top 5 or 10 'refiner' to do well but just better of living in reality I feel.
Edit: I see you said processing tailings which I initially missed, my bad. The tailings part would be mining but you arent going to find tailings high grade enough.