That isn't what I said. What I said was that you need a player doing a lot of without-puck work in order to have a strong possession player maximize his ability. I would think that all levels in between are possible, in any situation. The main point is that you simply can't separate two defensemen on a pairing and draw a conclusion. These aren't a bunch of individuals playing a team sport, a la baseball. These are teammates playing a team sport.
As for your specific instance, Doughty and Muzzin were pretty close on the season in hits (180-169; 6% diff) and blocked shots (91-82; 10% diff) and takeaways (16-14; 13% diff). These three stats are indications of "without puck" work. There's a variation in how individual official scorers tabulate these things, but for players on the same team, it works out. Staal and Stralman were close in hits (83-75; 10%) but far apart in blocked shots (84-64; 24%) and takeaways (41-29; 29% diff). If I were comparing the two pairings, I'd say that Doughty/Muzzin were more evenly sharing the load on the "without puck" efforts than Staal/Stralman. Your assertion of Muzzin as the "puck mover" of the pair isn't really borne out by the statistics. He's a more-than-capable "without puck" defender in his own right. That's not to say that Stralman isn't, just that Staal handles more of that duty than he does. I will say that the two of them seemed to share the load a fair amount more in the playoffs. Stralman was great.
McDonagh/Girardi is an interesting one to look at in this aspect. Girardi is way in front of McDonagh on hits and blocks, but McDonagh has way more takeaways. It's an indication of their particular skill sets.
Worth noting that McDonagh had the most giveaways of the top-4, both playoffs and regular season. His takeaway stats in the playoffs were ridiculously higher than anyone else on the team. He had 20, the next had 8.