DP is a mathematically term describing certain problems. It does not state that you need to save all solutions to sub problems. If you do have a DP problem, the fastest way to solve it is with recursion and memoization as needed because of the properties of the problem.
I am not arguing with this. In my comment my intend was to show that the distinction between the memoized top-down approach and bottom-up (the approach that is usually taught as DP in a classroom) is significant in some memory optimizations.
