The BMC is definitly paper based (like a standrad filter) not foam. I've never oiled mine. The web site says it's washable. No mention of oil.
BMC Air filters
Do you know which one of those models you have?
It doesn't have a number of it and I didn't buy it but going on the dimensions I'd say it was the CDA70-150. (length 200 Diameter of airbox 150 Engine side tube diameter 70)
I've just taken it apart. The filter element is a kind of metalic gauze. I notice on the site that you can buy replacement elements. Mines filthy inside. Maybe i should buy a new element befroe putting it back?