I use the Chingford branch nearly daily for my commute (otherwise it's via Tottenham Hale) - in the event of yesterday a lot of them did stop at Cambridge Heath and London Fields for the sake of no 'via Seven Sisters' trains. Quite often the trains do skip Bethnal Green as well, especially when there is a 'delayed' departure off Liverpool Street.
By delayed I mean that the train is scheduled to leave later than usual on the clockface timable (03,18,33,48 past the hour). A good example of this would be the 0805 Liv St to Chingford, this would on the clockface timetable leave at 0803 instead. However as there is a 0803 departure using the same line, which is a Greater Anglia service to Cambridge only calling at Tottenham Hale on the way. This LO departure gets pushed back to 0805, skips Bethnal Green to make up time so that by the time it gets to Hackney Downs it maintains a consistent every 15 minute pattern. This helps to avoid clashes at the Clapton Junction (not sure if that's the name) where GA goes to Tottenham Hale.
Hope this helps.
Interestingly, a train I often get, the 0748 departure off LST does not switch tracks at Bethnal Green. It instead does this at Hackney Downs however it still skips Cambridge Heath and London Fields.