I'm still thinking about/searching why they work, but Paul McCartney uses them in "Uncle Albert/Admiral Halsey" right after, "Hands across the water, hands across the sky" before he repeats that line, there is this progression: F - Ab - Bb - C. It sounds really good!
I still don't know why the Ab works in the Key of C, but I know how the Bb works, but not the details of why (theory). In any Major key, normally the vii chord is diminished. In the Key of C, the B would be diminished (Bdim). However, in harmonic theory and practice, you may, in a Major key, take the vii chord, flatten it and make it a Major chord. So, in the Key of C, you may take the Bdim, flatten it, and make it Bb (Major). The Beatles do this at the end of Hey Jude, where they repeat the "na na na na's." The song is in the Key of F, so the vii chord is E-diminshed. In the Na na na repeats, their chord progression is: F - Eb - Bb - F (which is: I, bVII, IV, I).