In general, sounds like yet another Marriott Corporate mandated published benefit that in practice is difficult to deliver uniformly across all brands and franchisees.
Large hotels, especially FS with shops, restaurants and bars certainly generate much cash and hopefully procedures are in place to manage and secure cash whether its $100 or $100,000 on hand. I'm pretty potential criminals and Management have this long figured out.
Perhaps the "we're low" is the counterpart to the "we're full" lie often uttered? Both are easier to say then have to get involved and do some work?