Having subconsciously thought about this for a wee while, I believe "memory" exists in many many places in the DBMM rules. Off the top of my head (from memory?) a few more examples of "memory", in addition to the examples provided by Neil and Mike, include:
1) unreliable allies (continue to be)
2) spending PIPs to activate an unreliable ally (spent previous bound)
3) brilliant strokes (e.g. combat advantage - spent during movement; feigned flight - turning for free the next bound)
4) halting and spontaneous moves (sponno moves for non-halted troops & cannot halt troops who moved)
5) number of moves per bound (are counted and remembered for PIP cost purposes)
6) weather (can change each bound and is remembered from previous bound e.g. wind, rain)
7) time of day (is based on the previous bound etc)
8 ) rivers (their state is remembered, not retested every time you cross a river)
9) you cannot halt an Expendable that previously moved spontaneously, and
10) an element that made a march move cannot shoot
and I'm sure there must be more examples.
So personally I think statements such as "DBMM has no memory" cannot be supported by reference to the DBMM ruleset only. It is probably a concept relative to other (dare I say, irrelevant) rulesets. Your last example Mike of elements not having memory of how they got to where they are doesn't apply to routing elements (cannot shoot), and I would also say elements that made a feigned flight. In addition there is memory for impetuous elements that make a flee move (from memory they turn if impetuous)), plus you cannot halt an Expendable that previously moved spontaneously. Are there any other movement examples? I say 'movement' because this seems to be the area in which the concept of 'no memory' is used most.
I suppose one area of contention is forming a column. If you cannot form a complete column in your current bound, must you continue to try to form the column in your next bound? I have seen differing interpretations of this - one of which implies "memory". Any thoughts on that?
Any other contentious areas?
Andrew