I think Rizzo thought Williams was a leader. He wasn't. Dusty was a leader, but wasn't a strategist (neither was Williams). Bud Black would have been better than either.
I live in Maryland, work in DC, and follow the Nats and go to games now and then. I don't get the sense that fans are pining for Dusty. I don't think fans generally think that Martinez is responsible for the Nats problems. He has certainly struggled in some respects, but I think most of the supposed clubhouse grumbling is simply a reflection of the old adage that winning teams have great chemistry, while you can always find problems on teams that aren't winning - especially on teams that are expected to win, but don't.
Most of the complaints I hear from Nats fans are about the injuries and the players not performing. Murphy and Eaton both missed a big chunk of the first half - I think everyone expected the Nats to go on a roll once they were back, but it hasn't happened. And there's a good bit of grumbling about Stras not being about to stay healthy. And Harper having a bad year - at least in terms of BA (but still drawing a lot of walks - looks to me like he's been pressing, trying to make things happen, and chasing too many pitches out of the zone). Zimmerman has been awful (thank goodness they picked up Matt Adams), and catcher has been a year-long problem. I think the fans are a lot more focused on these things than they are Dave Martinez.