You've basically got it. Cold oatmeal is right too.
Two main things to consider. And they're both related to control.
The act of grinding meat hugely increases the surface area. This is a problem since
Bacteria and pathogens are now spread throughout the product, and have lots of surface area to grow on.
This problem gets really scary when you consider that problematic pathogens like e Coli are often spread from feces getting on meat during meat processing ( e.g. The intestines are cut open and poo gets on the meat, e coli in poo, now on meat). These are supposed to be caught and diverted, but that doesn't always happen. So they compensate with a wash e.g. Mild bleach solution). Then the meat goes to a processor who makes ground beef, in a HuGe batch, 10,000 lbs all mixed up before the machines get cleaned. The ground beef goes to distbribution and sits for a week. You go home and eat it and get food poisoning. Some people die.
That's why usda recommends cooking your burger until 165- to kill everything.
Think this doesn't happen? Go look up and see how often you get ground beef recalls. Often for e coli, in HUGE batches. Its scary.
You can buy meat thats not produced by the big boys, but you still have a potential problem.
By ensuring that the beef is ground recently, you're giving yourself a better chance of "cleaner" product.
This also dramatically affect a quality, oxidation and flavor. Fresh hamburger is 100x better within 24 hours. 4 days later and it turns grey. 7 days started turning green and sour.
Fresher is better. Exponentially better. You don't have to grind yourself, but if you're assured at its been ground that morning that helps a lot.
This affects two things
A) growth of bacteria and pathogens.