Logic behind the Statement on Non-Parametric models
Non-parametric machine learning algorithms try to make assumptions about the data given the patterns observed from similar instances.By not making assumptions, they are free to learn any functional form from the training data.

Unlike parametric approach, where the number of parameters are fixed,
in non-parametric approaches the number of parameters grow with
training data.

If your data set is too small or otherwise is a set that is not representative of the entire population, then your result will be biased in more ways than possible with parametric methods.
So,to get better results in Non-parametric machine learning algorithms we need large amount of data where relationship between features are not known.
While non-parametric machine learning algorithms are often slower and require large amounts of data, they are rather flexible as they minimize the assumptions they make about the data.