Thanks to everyone for the replies.
To re-iterate, the purpose of the original post was to highlight the distinction between two scenarios.
I think we are all in agreement that the first scenario of consecutive bookings under the same MR account should be combined into a single "stay", and even if there are two folios (under the same account) with a check-out/check-in between them that only a single arrival amenity is applicable.
For the second scenario I intentionally avoided including specifics so as to isolate the underlying general principle that physical occupancy is not equal to a "stay" as defined by the MR program.
Here is the relevant information from the Terms and Conditions:
Paragraph 2 under General Membership: "A “stay" or "qualifying stay" means all consecutive nights a Rewards Program Member registers and personally pays and stays at any Rewards Program participating hotel, for which the room is billed to the Member. "
Paragraph 6 under Earn Points: "No other person except the Member may earn Points for his/her Membership Account. Points for a room shared by two Rewards Program Members will only be awarded to one Rewards Program Member."
The only natural conclusion for consecutive bookings under two different accounts is that: (i) they are not combinable, and (ii) arrival amenity applies separately to each account. Moreover, while Member A may occupy the same room on each day, that person is only "staying" for the purpose of MR program on the date of the booking under Member A's account; and is not "staying" for the purpose of MR program on the date of the subsequent booking under a different Member's account.
Of course, the bulk of all cases will be Scenario 1: For example, business travelers who normally reside at a private residence and stay alone at a hotel briefly on a business trip will only have one MR account in play, and thus any consecutive bookings will either be combined into a single stay or separate folios (for leisure extension) will still not be entitled to another arrival amenity. Another example is leisure travelers, where typically a family which normally resides at a private home and goes as a family on holiday will have just one MR account for the whole stay regardless of whether it consists of one or multiple bookings, and accordingly in the latter case they should be combined into a single stay with only one arrival amenity.
There are, however, some situations which give rise to Scenario 2: For example, students, colleagues, or family members who all have individual MR accounts may make separate bookings for a property on consecutive periods (nights/weeks/months) but share a room for the whole extended period. In this case each Member is entitled to the credit/points/amenity for the room on the dates of their own account booking, regardless of who else physically occupies the room.
The solution to avoid system confusion and retain clarity of proper credit distribution is to only have a single MR account number on the hotel's folio for a particular booking. So, if Member A occupies the same room under Member B's account for a subsequent consecutive date, Member A's folio should be closed after the first booking and the latter booking should have only Member B's account number.
Here are several problems which can arise if this simple procedure is not followed -- especially in the case where Members A+B are occupying a room/suite for a longer period (eg. 1 month).
(i) Since a Member can only receive credit for a particular night from a single property, if Member A's number is wrongly attached to a booking under Member B's account at Hotel X for that whole month, then Member A is not able to travel and stay (for program credit) at another Marriott property anywhere in the world throughout that period.
(ii) To avoid the problem as described in (i) above, Member A stays at an SPG property for a short overseas stay during the period of the 1-month booking at Hotel X under Member B's account. Upon a late-night return to Hotel X, Member A books a second room for 1 night under Member A's own account. Upon check-out of that second room the next morning, and return to physically occupying the first room still under Member B's account, if Member A's account number is wrongly attached to Member B's room then the Marriott system will not treat Member A as having checked-out from the second room until the next physical departure by Member A from the hotel. This results in a total distortion because Member A should only receive credit/points/amenity for 1 night in the second room, and Member B should receive the credit/points/amenity for the whole month in the first room.
While obviously not a typical or broad experience for most Members, both of the above issues actually arose recently precisely because the hotel erroneously believed that they must attach the MR numbers for all adult occupants rather than maintaining only one account number per folio -- thereby failing to distinguish between consecutive physical occupancy and a "stay" as defined by the MR program.