It's unhealthy when they allow it for a long time, benefit from it, and then pull the rug out from under them once they believe it is in their financial best interest to do so. It's exactly the same as your Twitter and Facebook developer examples.
Developers were monetizing the Twitter platform until Twitter pulled the rug out. Facebook has similarly neutered their API to the point where it is nearly useless, and many businesses were crushed in the wake of the changes. You seem to be saying that it's only unhealthy when developers are affected, but that isn't the case. Developers have no "inherent right to succeed on the good graces of another business allowing them to" either, yet you see that as unhealthy.
Publishers and developers are just users of the system, getting crushed when Facebook doesn't believe it's getting a big enough cut. I would also argue that Facebook actively blocking the sharing of external content that its users choose to share with each other simply because they aren't getting their cut is different than the affected businesses believing they have an "inherent right to succeed on the good graces of another business". Businesses that don't directly do anything on Facebook will be affected by this, because if their visitors wish to share their content, they will likely attempt to share it through Facebook.