My main response to this is: just because we can't always use content-addressable links doesn't mean we shouldn't use them where we can. I'm sure you see where I'm going with this. When pirate movie websites have a 1000x more rock-solid way of identifying content than the NY Times we have a problem.
But even in the most inhospitable situations like the one you describe we can still do better. Content-addressability won't help, agreed. How about promoting UUID style non-human readable paths instead? One of the reasons links change is that the content changes slightly and the name goes out of date. Perhaps in your case legal says "these prices may be up to ten minutes out of date, we can no longer call that path /prices/current/feed". If the path was /3824-3822-4864 this wouldn't be a problem. Information about what that endpoint returns can be placed in a description field or in the docs where it can be kept up-to-date without breaking links.