Difference between a Fixed Point and a Limit Point in implementations of the Renormalization Group (RNG) in Large Eddy Simulation (LES) model

Question

In the introduction of this paper, it is explained that and how the application of a dynamic subrid scale model for turbulence into a large eddy simulation (LES) model corresponds to doing one renormalization step in a renormalization group (RNG) analysis.

However, when implementing the renormalization group into a LES model to obtain subgrid scale parameterizations, the rescaling step is left out. If I have understood this correctly, the rescaling leads to the fact that finally, after $k$ renormalization steps one considers a infinite in space domain which is needed to define scale invariance and therefore fixed points of the RNG flow. The neglect of the rescaling step leads to the fact, that the limit obtained in the model for $k -> \infty$ is not a (or does not have to be?) a true fixed point of the RNG transformation and is called a limit point to distinguish it from a conventional scale invariant fixed point.

My question now is: Can the difference between such a "true" scale invariant fixed point of the RNG flow and the limit point, obtained ofter a large enough number of renormalization steps lead to a "misbehavior" of the dynamic subgrid scale parameterization, such that for example an expected Kolmogorov fixed point is missed and the turbulent kinetic energy spectrum shows not the right scaling ?