We've had these discussions in the past. It seems now most people are aware of the fact of dual-certification and how to get around it.
If you really need to convince him, tell him '316' is in the designation '316/316L'. He cant ignore that.
Otherwise, draw a picture of the chemical range of elements in 316 and 316L, show the overlap, and explain why you can benefit from the 'stronger 316', and chemically more attractive L-grade 316L.