I get the argument that pulling from a distribution is a form of curve fitting. But unless I am misunderstanding, the claim is that it is a curve fitting / interpolation between the training data. The probability distribution generated in inference is not based on the training data though. It is a transform of the context through the trained weights, which is not the same thing. It is the application of a function to context. That function is (initially) constrained to reproduce the training data when presented with a portion of that data as context. But that does not mean that all outputs are mere interpolations between training datapoints.
Except in the most technical sense that any function constrained to meet certain input output values is an interpolation. But that is not the smooth interpolation that seems to be implied here.