I would rather say that there is no theory behind it but rather a kind of style and a tendency to connect chords in the shortest way possible.
That meaning - every note of a chord has to go to the closest note of the following chord with the least possible resistance -> shortest movement and easy to sing if you see each chord progression as different lines of melodies that happen to (vertically) form chords on their way through time.
So if you consider this as THEORY I can give you some explanation:
The closest note for the the 3rd (D) of your Bb chord (SUBDOMINANT or IV) would be the 5th (C) of the (most likely) following TONICA (root) chord F (F A C).
There is only one way to get closer to your TONICA chord and this is to flatten the 3rd (D) of your Bb chord to a minor 3rd (Db). Now you have the perfect chromatical line in your imaginary melody D - Db - C...
Least resistance - shortest and fastest movement possible ;-)))
Just look what those Jazz-people out there are doing (since the times of J.S.Bach - the grandmaster of them all):
II m7/9 - V 9/b13 - I maj9 - I 6/9
Dm7/9 - G9/b13 - C maj9 - C 6/9
Or the hardcore version:
II m7/9 - bII b5/b13 - I maj9 - I 6/9
Dm7/9 - Db b5/b13 - C maj9 - C 6/9
Chromatic lines all over the place - even in the base line... ;-))) - but of course this changes the style and character of your music. And - of course - the G in the second chord of the hardcore version is actually a double flat A ('Abb')
But would you ever consider Bach to be the greatest 'Jazzer' ? No?
Well then get yourself some Bach-scores and read all the polyphonic lines of his Fugas and Concertos vertically (in chords). This will let Charlie Parker appear as a composer of lightweight children songs. ;-)
But seriously - if you want to learn about real application of chords in music forget about theory-books. They only explain what has already been written long time ago. So listen and compare the scores at the same time.
As once one said: Talking about music is like dancing about architecture!
Go for the real thing. It's already there...
EDIT: And by the way - in the progression F A Bb Bbm - the A chord instead of the usual Am is doing the same. Chromatically progressing line from C-C#-D. And the Bb-Bbm is reversing the same pattern. So you get a nice chromatic melody C-C#-D-Db-C...
By doing -> F F7/#5 Bb Bbm you would get the same C-C#-D-Db-C line. Same principle but different chord progression...