For SEO Purposes it makes no difference if the pic is a logo or something else.
For brand awareness, getting the logo in the citations is a requirement.
You should point out to your customer that getting his logo out there will increase band awareness, helping people to remember his service or product even when they cannot remember his name. In fact that is why logos exist.
It is good business to get that brand name and logo out there, it is good business to let your customer know the benefits before he makes a decision, and it is smart business to do what the customer wants after giving him all the options, even if what he wants is stupid.