In case the organisation is basically a tenant in multi-tenant application I would leave it out of the API and resolve it in another way, but if it is not I would leave it in. Does that make sense?
I'd really recommend putting the organization name in the content of the page in that example. Users don't really look at URLs, browsers de-prioritize them and often only display part of the URL.
Also, depending on front-end implementation the REST API URL may not be displayed in the URL bar. A single page app may use example.com/#create-article for posting an article. A mobile app wouldn't even have a URL bar.
One solution is to always pass the intended org along in the POST, but requires something disciplined and nesting POST /org/A/articles is one way to do that.
Thanks!
I guess the one case where it might still make sense to have the organization ID in the path is if users can be in multiple organizations and some APIs involve listing all of a given resource for a certain organization.