A thought struck me while I was outside. Luckily it hit me in the head, so it didn't hurt.
Since the only use I have for stock is gravies, soups and other things that I bring to a boil.... Do I really need to boil it ahead of time?
First, if it were I, I would toss it. {omitting thoughts on pre packaged broths}
Yes, boil it before you put it in the cooler.
Refrigeration does not stop growth, only inhibits it.
What leaving it on the counter overnight did was give the bacteria a head start. You need to kill it, or as much of it as you can.
The rule of thumb is, 4 hours above 40 degrees or a week in the fridge, Doing KIS math, the 4 hours on the counter aged it a week.
And you know, bacteria don't reproduce lineally, they reproduce geometrically.