I think you're probably right, although LVG may also have a more general problem breaking down teams that set up defensively. Of course, every team will struggle to some extent to break down a parked bus, especially if you're dealing with defenders of high quality like City possesses. But LVG's commitment to playing two defensive midfielders at nearly all times (two of the Schneiderlin/Schweinsteiger/Carrick trio) really makes things difficult. When they had Shaw and Darmian at FB, this problem was ameliorated because they were pretty effective attacking down the wings and through overloads at the corner of the box. But with Shaw hurt and Darmian now seemingly out of favor, they're starting Valencia and Rojo, neither of whom offer much in terms of breaking through a deep, organized defense.
