The key is I distinguish between an API which IS the business - something like a Twilio for example - and an API which lets you leverage a business's other assets in a way that might one day be cut off - like a Twitter.

You are safe to build on top of something like Twilio because the service is the API and API consumers are the customers. Consumers of Twitter's API are not customers of Twitter and should not be surprised Teotter does not treat them as such.

You are either the customer or the product. If you are neither you are in a precarious position.