Hmm... is it so hard to understand that not facebook page for a business is part of an organisation's plan?
Having a facebook page does not mean doing social media.
Having, or not having, a facebook page pages boils down to what the marketing plan of the organisation is. Or more importantly, what the content marketing plan is.
Is your facebook where your audience is? Can you provide a consistent stream of content that is of value to the audience? How does facebook factor into the overall marketing plan?