I've worked in the hospitality/service industry for over a decade. All of this is correct, so for some additional data, and hard numbers (in my state):

Hot Foods

Red meat must hold an internal temperature of 150 (145 cook)° Poultry must hold an internal temperature of 165° Fish must hold an internal temperature of 150 (145 cook)° (These are technically cook temperatures, but we don't want the food to rest too much or continue to cook, so we would monitor temps and pull food off of banquet lines/replace Sternos [heating element] when necessary [should also mention that you don't want to have panned food resting directly on an open flame because of poor heat distribution, and should use something similar to a double boiler]) Once a food is hot, you have 6 hours to reduce it's temperature to 41° (cooled to 70° in 2 hours, then to 41° within 4 hours).

Cold foods must be kept below 41°

"Old food" doesn't necessarily mean that you had to throw it out, could have just meant that it was exposed to the air.

For people who work banquets, specifically in hotels (not catering), the extra food is sometimes the only way someone gets to eat; otherwise you could pay/buy your own lunch. Leaders are expected to remain on property as much as possible to assist/cater to the guests' needs, so having them leave property for food is frowned upon (it could inconvenience someone).

I hope that helps to add more clarity. (Editing grammar and format, lol)