Having formerly worked at Subway's HQ I can confirm that there was no actual requirement or obligation to eat Subway (it was provided free of charge, daily in the building's kitchen) but there was once an initiative asking employees not to order-in food from outside merchants. It never gained any traction. As to the origin of the discussion in this thread, I have heard rumor of Pepsi/Coke exclusivity agreements but I think its more an urban legend than anything else. These sort of things usually apply only to celebrity sponsors or, in the rare case of a company employee, someone in the C-Suite.

If a company wanted to impose such a harsh restriction on a floor level employee, especially something as wildly prohibitive as mandating what kind of car someone could buy (in the Honda example), they would need to compensate the employee for accepting such a restriction or provide an extraordinary discount.