The image patches do not span the entire space of pixel values, and also not the smaller space of patches from natural images. They consist of the highly restricted set of patches that passed the first 3 stages of SIFT.
Low recall rate at high precision is acceptable for real-world applications. Recall of 5% at 1-percision of 20% - about 1000 keypoints in image, of which 50 are reliable matches. Sufficient for applications like image retrival.
Hypothesis – First several components of the PCA subspace are sufficient for encoding variations caused by keypoint identity, while the later components represent details that are not useful, of potentially detrimental, such as distortion from projective wrap.