Then putting it under a brand that for so long has been associated with (and pushed on, and designed for) internal enterprise documents or other sensitive/personal docs might not've been the best move?

I don't know that there's a "social docs" brand, to figure out what it would call itself; but if MS exerted the minimal effort to understand its audience (which is required of any tech company that sells to domain experts who are more occupied with their work than what the workspace is configured to do), it wouldn't take them long to figure out how to pitch things to those users to accomplish whatever it is they're trying to do.

My guess is docs.com will be merged into LinkedIn at some point; that would largely solve the problem since people already have a mental model of LI's purpose and sharing semantics, etc. (or at least the cost of acquiring one is amortized over other services/features that are part of LI)