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?
In some cases there might be a next stage of complexity where you have users with access to multiple tenants who are browsing them in different tabs. Then putting the organization as the top level in _every_ URL helps signal intent; otherwise you have to take other precautions that someone isn't on a tab with Organization A, clicks "Post new article" button (-> POST /articles) and happens to have their session logged into Organization B and so creates the new article ere.
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.
In the above example the user saw they were on an Org A page and clicked Create intending to create an article in Org A, but sometime after they loaded their Org A page their “current tenant” session variable had been switched out from under them by a different tab.
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.
In a multi tenant application you will strictly rely on the authenticated and authorized principal and the company id in which it resides when making every request. So baking it into the route is not great because you're never going to trust the value in the route anyway, you have to refer to the claim in your request.
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.