Intuition of applying PCA before logistic regression

I came across this paragraph about logistic regression with PCA in Kevin P Murphy's book on Machine Learning. If we use PCA first, then use logistic regression afterwards, although overall, this is still representable as a logistic regression problem, the problem is constrained since we have forced linear regression to work in the subspace spanned by the PCA vectors. Consider 100 training vectors randomly positioned in a 1000 dimensional space each with a random class 0 or 1. With very high probability, these 100 vectors will be linearly separable. Now project these vectors onto a 10 dimensional space: with very high probability, 100 vectors plotted in a 10 dimensional space will not be linearly separable.