selling an idea - urban legend?

Quite some time ago, I heard two stories about genius ideas. Both of them were allegedly coming from outside the company and sold to big corporations, with those ending saving a lot of money (and also paying generously to the person coming up with the idea).

The first story was about the toothpaste tubes colgate produced - the idea was to increase the circumference of the pipe of the tube, and since people use the same length of toothpaste to cover their toothbrushes, they will end up using more toothpaste.

The second was similar and mentioned saving cost of matchboxes, by only covering one edge with the striking surface, instead of two.

I couldn't find any authoritative sources of information about these, but I think both are famous enough, and I just couldn't use the right keywords. Are these stories true? or an urban legend?

And if they are true, would it be possible today to sell just an idea in a similar way?

Both seem like urban legends to me, but it is hard to know for sure. I also heard one about cars, where in the UK all cars used to have two reversing lights, but someone suggested that the manufacturers just have one and they could save millions.

If you had such an idea, it would be difficult to sell as you'd have to give the idea away to negotiate, leaving you in a weak position, or somehow convince someone (BigCorp) to extend you a lot of trust.

If you look closer, those stories have a few things in common: the ideas were easy-to-understand and easy-to-implement and had a huge obvious impact on the company's bottom line. They weren't suggesting to make a dramatic change to the process or to implement a new technology. Such ideas are definitely great commodities to sell.

However, you can't just waltz into a CEO's office and present them - you still have to work your way to the right people and protect yourself legally from someone else claiming it as theirs.

Added: FWIW, these ideas could've been suggested by an employee who was just rewarded generously.