Many recent improvements in .NET performance are enabled by reducing or removing allocations in hot paths, so the GC has to do less work¹. The point was mostly that the .NET GC can get away with not being as advanced since it commonly has to do less work than in Java anyway. C# gives the developer more low-level control over what actually runs on the CPU in the end, so there's a slight shift in responsibility for performance from the JIT/GC towards the developer (although the latter two also improve, of course).

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¹ Plus a number of algorithmic improvements and the ability to leverage specific CPU instructions that help as well.