In a data warehouse, should a measure be based on a fact or a dimension?
The problem with contrived examples like the one you provide is that whatever answer you find, it won't be helpful in a real life situation. "A number of distinct customers" is useless as a measure, because it doesn't represent anything a business would care about.

Now, there could be more useful measures, such as "a number of distinct active customers per month", or "a number of distinct customers per geo", or "monthly customer churn", and from their very definitions you immediately see what information is required to compute them.