You might have encountered hotel employees who are confused. My guess is that at most full-service hotels with club/concierge/executive lounges, the majority of guests using the lounge have access based on Elite status, not based on having paid for a room on a club/concierge/executive floor. Also, most guests who have paid for such a room are probably business travelers with generous expense accounts. Three adults with "authorized" access to a lounge (based on room type) would be a rarity.

Special floors are becoming more rare.

When I've stayed at hotels with an M Club Lounge, there has not been an M Club Floor or other club floor. There were two ways to get M Club Lounge access: (1) sufficiently high Elite status, in which case access was for member + 1, or (2) pay for an M Club Lounge access pass, available to any guest staying in any room, for a set amount such as $40 per day for up to two guests.