I'd imagine it would be illegal for Vanguard to implement in the way that Betterment does. Betterment buys exchange traded securities to allow their customers to participate in the underlying mutual fund. They can basically jump from a Vanguard ETF to a Schwab or iShares ETF of a similar market. I'm reasonably certain it would be illegal for Vanguard to purchase a competing fund's ETF as it would be directly affecting the business of a competitor.
In fact, I'm not even sure how Vanguard could do this in any manner that would be customer facing.