Well, in my experience and also in the book "Lern Yerself Scouse" it clearly is OK for chip buttie to have no accompanying grease. This of course assumes that the chips themselves are greasy and not those poncy shoestring things.
I agree fully about mayo, but some southerners do not.
What happens if I ask about chips and gravy? It's a delicacy unknown in many southern parts, even including Birmingham.