Unless your company was advertising the fact they lost money on every sale(and if it was still private why would it) how are the downstream customers to know that it didn't really figure out a way to create the widget cheaper than all the competitors?

If they were the only source of the product at that price, and they couldn't pay more for it... Then it seems obvious to assume something will go wrong eventually, collapsing the whole house of cards.

If your margins are that tight, any delay in a shipment will decrease your profit too much and risk the whole thing.

They don't need to know there's a current problem, only that any problem will collapse everything.

How many competitors do you think someone has when a customer “built their whole strategy around our continued existence”

Enough so that they couldn't raise the price to break even?