I was having a bit of a think about this earlier today on the bus on the way home (very relaxing, sitting on the bus!).
One of the underlying concepts of DBMM is that there is intended to be no need to record the status of individual elements. Therefore whatever decision is reached about the status of the dismounting element, there shouldn't be any need to record anything.
Anyway, here's my thinking...
1. My attitude is that a mounted element can only be covered by point (a) if its dismounted version could move into the difficult terrain in a single tactical move. In other words, you have to be close to a piece of difficult terrain (which, obviously, must be occupied by enemy of whom it's aware).
2. Once the mounted element dismounts, it's free to go wherever it wants and do whatever it wants. There should be no obligation (except impetuousity) on the dismounted element to enter the difficult terrain, or to remount.
The first thing people will see on reading these points is that it allows you to use enemy-occupied difficult terrain to dismount troops who ordinarily wouldn't be able to dismount, and that those dismounted troops could then move off in some other direction to attack somewhere else. Yes, and I don't have a problem with that. If nothing else, dismounting in expensive in PIPs; if you're willing to spend PIPs to move mounted troops up to a piece of difficult terrain in order to dismount them at a rate of no more than three elements a bound, just so that you can then move them somewhere else to attack, then I'd consider I've won the exchange - that's an awful lot of PIPs you've used, and bounds you've used up, to set up that attack. Meanwhile I'm doing things elsewhere on the table.
