The purpose of the "On The Run" bag is to allow someone who does not have time to sit down for BK to get something to go. Nice concept. I think that it is rather tacky for someone to sit down for a full BK, then grab a bag on top of it. I am not sure if that was the OP's case or not though.

The sign at the front desk explicitly says "Monday through Friday from 5:30am to 10am." The FD staff member was doing a favor for the OP's parents by making up a bag on the weekend.

It may have been bad taste for the employee in the back to yell out that the bags are only supposed to be out during the week, but considering that the other front desk employee was doing them a favor in the first place by giving them a bag on the weekend I don't think that this would be grounds to complain.

As to whether the bags are meant for business travelers: it is not explicitly stated anywhere as such. You could assume that since HI's only offer them during the week, and since most HI's are in corporate markets, that they are tailoring the program to the busy business traveler. I am sure that Hilton is more tactful than the back office employee was by yelling out that they are only for business travelers.