Not really - this rule of thumb is generally applicable to bulbs, corms, and some rhizomes. In fact, many flowering shrubs flower on growth made the previous year, so the time to prune those is immediately after flowering has finished, to give the plant time to put on some growth before winter arrives. There's a rule of thumb for flowering shrubs - if it flowers before June, prune right after flowering - if it flowers after June, don't, prune in late autumn or early spring instead, but there are lots of exceptions.
The point about bulbs and corms is they're storage organs - the flowers and leaves appear at a certain point in time, and only for a short time period (spring bulbs/corms particularly) in the year, and while the leaves are present, the plant is able to gather enough nutrients to store in order to prepare for flowering the following year. The foliage then dies down completely some time after the six week period passes. There are other bulbs with different habits - Nerine bowdenii has leaves all summer, which then die back and the flowers usually arrive when the leaves are gone. Allium is similar.
Paeonies have tubers though - these are also storage organs, so it isn't wise to chop down all the foliage as soon as the flowers are over, its better to leave it in place for a few weeks for similar reasons. Mostly people do leave it in place, the leaves are not unattractive anyway.
Other plants on ordinary roots don't have such a system in place, often keeping their leaves all summer (perennials) regardless of when they flower. Take Aquilegia as an example - once the flowers are finished, its perfectly alright to chop the whole plant down if you want to rather than just the flowered stems - it will produce new leaves pretty quickly anyway, unlike daffodils or crocus, and will flower the following year regardless.