This is a very naive take. It's so common to get big companies in as signal to others, or just match the current provider you have for X or offer you a cheap price to then hike it up next year, among many other sales tactics. It's definitely not "always ask for the most if the company has a lot". In fact I'd say companies with more money are more likely to get early good deals.

Have you done procurement yourself at the type of companies you describe?