I just looked at the actual rules. There nothing saying you only get credit for one hotel per night. The requirement is simply that you must pay for and stay in one of the rooms. It does not say that you must occupy the room non stop, or that you can't also get credit for a room that you simultaneously use at another hotel. If you stay in the room, you're good.
A Member is eligible to receive Points/Miles for staying at participating Marriott brand hotels or Ritz-Carlton hotels for his/her room and up to two additional rooms. At least one of the rooms must be reserved and registered in the Member's name and the Member must pay for all rooms, which payment arrangement must be requested at time of hotel check-in. The Member must also stay in one of the rooms. To ensure Points are automatically posted to the correct Membership Account, the Member's Rewards Program Membership Number must be present on his/her room folio and up to two additional rooms, as applicable.
Now it's true, they don't define "stay". Obviously, they don't mean never leaving the room. They mean what a normal person would think it means, which is to occupy the room for your personal use. It's entirely possible to occupy several rooms in several different places over the course of a day, and to want to rent several different hotel rooms in the process.
If they wanted to say "You will receive credit for at most one one hotel per night" they could easily have said that. But they didn't.
Inconveniencing, alarming, and embarrassing a good customer by suspending their account for this is madness.